Tag Archives: addition & Subtraction of matrices
THE BANKING SYTEM & COMMON MAN FACILITATION
The banking system is a network of financial
institutions that facilitate the flow of money within an economy. It consists
of various types of banks and financial entitiesΒ that provide servicesΒ such as
accepting deposits, making loans, offering financial products, and enabling
transactions. The primary functions of the banking system are to:
- Facilitate Payments: Banks provide a secure and efficient way to
transfer money between individuals and businesses through various payment
methods like checks, electronic transfers, credit and debit cards, and
mobile payment apps. - Lend Money: Banks issue loans to individuals, businesses, and governments to
support economic growth. This lending helps finance investments,
purchases, and other economic activities. - Accept Deposits: Banks offer a safe place for individuals and
businesses to deposit their money, which in turn helps create liquidity in
the economy. - Act as Financial Intermediaries: Banks pool resources from depositors and
lend them to borrowers, effectively channelling funds from those with
excess money to those in need of capital. - Manage Risk: Through various products like insurance, derivatives, and savings
accounts, banks help individuals and businesses manage financial risks.
Types of
Banks in the Banking System
- Central Banks: These are the primary regulatory bodies of a
countryβs banking system (e.g., the Federal Reserve in the U.S., the
European Central Bank in the Eurozone). They control monetary policy,
manage the countryβs currency, supervise commercial banks, and serve as a
lender of last resort. - Commercial Banks: These are the most common type of banks,
providing services to individuals, businesses, and governments. They offer
checking and savings accounts, loans, and other financial services. - Investment Banks: These banks specialize in large-scale
financial transactions like mergers and acquisitions, underwriting new
securities, and facilitating capital raising for corporations. - Credit Unions: Member-owned financial cooperatives that
offer similar services to commercial banks but often have more favourable
terms for their members due to their non-profit nature. - Savings and Loan Associations (Thrifts): These focus on accepting savings deposits and
making mortgage loans. - Cooperative Banks: These are financial institutions owned and
operated by their members, often serving local communities or specialized
groups.
The banking system is critical for economic
stability and growth. By providing credit and liquidity, it supports consumer
spending, business expansion, and investment. Additionally, it helps control
inflation and promotes financial stability through regulatory oversight and
risk management.
The systemβs stability is vital for preventing
financial crises. A failure in the banking system can lead to a credit crunch,
where businesses and consumers are unable to borrow or obtain funds, leading to
an economic downturn. Therefore, central banks and governments often intervene
to protect the banking system and maintain public confidence. Therefore The
banking system is a cornerstone of any economy due to its pivotal role in
facilitating financial stability, economic growth, and wealth distribution.
Here are the key reasons why the banking system is vital:
Β
- Banks connect savers (individuals or entities
with surplus funds) with borrowers (individuals, businesses, or
governments needing funds). - This process ensures that money is channelled
into productive uses, such as business expansion, infrastructure
development, and education.
2.
Facilitating Investments
- By providing loans and credit, banks enable
businesses to invest in new projects, technology, and human resources. - They also allow individuals to make
significant purchases, such as homes or education, which contribute to
long-term economic productivity.
3.
Supporting Economic Growth
- The banking system provides the capital needed
for businesses to operate and grow. - It encourages entrepreneurship by offering financial
resources for start ups and small businesses, which are often key drivers
of job creation and innovation.
4. Payment
Systems and Transaction Efficiency
- Banks offer safe and efficient methods to
facilitate payments, such as checks, wire transfers, and digital
transactions. - This reduces the reliance on physical cash,
lowers transaction costs, and increases the speed of economic activities.
5. Money
Supply Management
- Through credit creation and deposits, banks
influence the money supply in the economy. - Central banks use the banking system to
implement monetary policies, such as controlling inflation, stabilizing
currency, and ensuring liquidity in financial markets.
6. Financial
Stability
- Banks promote confidence in the financial
system by offering secure places to deposit money and access credit. - Deposit insurance (offered by institutions
like the FDIC) and regulations ensure that peopleβs savings are protected,
enhancing trust in the system.
7. Wealth
Distribution
- Banks help reduce economic inequality by
providing access to financial services for all segments of society,
including loans, savings accounts, and microfinance for low-income groups. - This access enables broader participation in
economic activities and promotes social mobility.
8.Β Crisis
Management
- During economic downturns or financial crises,
the banking system acts as a stabilizing force. - Central banks, as part of the banking system,
provide liquidity support and act as lenders of last resort to prevent
economic collapse.
9.
Facilitating International Trade
- The banking system enables cross-border trade
by providing services like letters of credit, foreign exchange, and trade
finance. - This support allows businesses to expand
globally and contributes to a countryβs economic integration with the
world.
10.
Encouraging Savings and Investment
- Banks encourage savings by offering
interest-bearing accounts, which helps individuals accumulate wealth over
time. - These savings are reinvested in the economy,
fueling a cycle of growth and productivity.
In summary, the banking system is the backbone of
any economy, ensuring that resources are allocated efficiently, transactions
are facilitated smoothly, and economic stability is maintained. Without a
robust banking system, economic activities would stagnate, and growth potential
would be severely constrained. Then banking system also effects the common man
in various ways as The banking system plays a crucial role in improving the
lives of common people by providing financial services that enable economic
participation, security, and convenience. Hereβs how it benefits individuals in
any country:
- Banks offer secure accounts (savings,
checking, and fixed deposits) where people can store their money safely,
protecting it from theft or loss. - Interest earned on savings helps individuals
grow their wealth over time.
2. Access to
Credit
- Banks provide loans for various purposes, such
as buying homes, vehicles, or starting small businesses, enabling
individuals to achieve financial goals. - Affordable credit facilities, like personal
loans and microfinance, empower people to invest in education, healthcare,
or entrepreneurial ventures.
3. Easy and
Efficient Transactions
- Banks facilitate day-to-day financial
transactions through tools like debit/credit cards, mobile banking, and
online payment systems. - Automated Teller Machines (ATMs) and
point-of-sale (POS) systems ensure cash availability and quick payments
anytime and anywhere.
4. Financial
Inclusion
- Through initiatives like zero-balance
accounts, rural banking, and mobile banking services, banks extend
financial services to underserved communities. - Government schemes often use banks to
distribute subsidies, pensions, and social welfare benefits directly to
citizens, reducing leakages and ensuring transparency.
5.
EncouragingΒ Savings Habits
- By offering recurring deposit schemes, fixed
deposits, and investment-linked savings plans, banks encourage disciplined
savings habits. - These services help individuals prepare for
future needs like retirement, education, and emergencies.
6. Insurance
and Wealth Management
- Many banks provide insurance products, helping
individuals secure their families against unforeseen risks like accidents,
illnesses, or job loss. - Banks also offer investment options like
mutual funds, bonds, and retirement plans to help people grow their wealth
systematically.
7. Digital
and Mobile Banking
- Digital banking services enable people to
access their accounts, transfer money, and pay bills conveniently from
their phones or computers. - Mobile wallets and payment apps have made
financial services accessible even in remote areas.
8.
AffordableΒ Remittance Services
- Banks facilitate domestic and international
remittances, enabling individuals to send money to family members securely
and affordably. - These services are particularly beneficial for
migrant workers and rural households.
- Many banks run financial literacy programs to
educate common people about saving, budgeting, borrowing, and investing
wisely. - This helps people make informed financial
decisions and avoid falling into debt traps.
10.
Employment Opportunities
- Banks createΒ direct employment opportunities
for millions of people. - Indirectly, they enable small businesses and
entrepreneurs to thrive, contributing to job creation in various sectors.
11.
Supporting Small Businesses
- Banks provide loans, credit lines, and
business development services, helping small and medium enterprises (SMEs)
grow. - These businesses often employ local workers,
benefiting the broader community.
12.
Facilitating Ownership
- By providing affordable housing loans and
vehicle financing, banks help individuals achieve ownership of assets,
improving their quality of life.
13. Economic
Empowerment of Women
- Many banks run programs focused on providing
financial access to women, promoting their participation in economic
activities and entrepreneurship.
14. Crisis
Management
- During emergencies, such as natural disasters
or pandemics, banks help by extending loan moratoriums, restructuring
debt, and distributing government aid efficiently.
In essence, the banking system serves as a bridge
between individuals and the broader economy,Β empowering people to manage their
finances better, achieve their goals, and contribute to the nationβs economic
growth.
Β
Statistics Topics with Practical Solutions
Primary & Secondary Data Collection ways
Hi there ,
Letβs discuss the collection of data for any purpose . There are two types of data collection methods 1. Primary data collection which the investigator himself collect for its own usages .and 2. Secondary Data which is collected by organisations for fulfilling their own purposes like Professional Bodies , surveys , reports and for various researches .
In Statistics data can be collected by various ways like
1. Directly interacting with the Groups of People .
2. the person can appoint local agents which are collecting the information and pack it up to Investigator or the person who requires the data
3. by oral conversation with third persons regarding the use of certain product which is producing .
4. via making scheduled visits to the concerned general respondent and ask him few questions & collect the data
5. the next is creating questionares and spreading it in various ways like personal interviews , emails , social media or other tele ways through which the data is collected .
The data is the Prime aspect of generating any reports and accurate measures must be taken to collect and arrange it .
thanks
Want to MASTER Derivatives? Watch This Now : Lecture II
Cost Curves: Your Guide to Microeconomic Success / Cost Curve Analysis
Letβs Discuss cost curves in Micro Economics there are two types of cost curves U shaped cost curves in
Traditional Theory of Cost and L shaped cost curves in Modern Theory of cost we can discuss them one by one :
The traditional theory of cost, also known as the βcost-output relationship,β explains how a firmβs costs change as its level of output changes. It is divided into two key parts:
it can be seen via this link and I will describe them in written form as well
Short-Run Cost Analysis
Long-Run Cost Analysis
1. Short-Run Cost Analysis
In the short run, at least one factor of production (usually capital) is fixed, while other inputs (like labor) can be varied. The traditional theory breaks short-run costs into several categories:
Total Fixed Cost (TFC): Costs that do not change with the level of output (e.g., rent, salaries).
Total Variable Cost (TVC): Costs that vary directly with output (e.g., raw materials, labor).
Total Cost (TC): The sum of TFC and TVC:
TC = TFC + TVC
Average Fixed Cost (AFC): TFC divided by the quantity of output:
AFC =TFC/π
AFC decreases as output increases because fixed costs are spread over more units.
Average Variable Cost (AVC): TVC divided by the quantity of output:
AVC = TVC/π
Average Total Cost (ATC): The total cost per unit of output:
ATC = TC / π = AFC + AVC
Marginal Cost (MC): The change in total cost when an additional unit of output is produced:
MC = ΞTC / Ξ π
Marginal cost helps determine the level of output at which profit is maximized.
In the short run, costs exhibit a U-shaped behavior due to the law of diminishing returns. Initially, as production increases, marginal costs fall because of increasing returns to variable inputs. Eventually, marginal costs rise as inputs become less productive.
2. Long-Run Cost Analysis
In the long run, all factors of production can be varied, meaning there are no fixed costs. The firm can change its scale of operations. The traditional theory of long-run costs focuses on economies of scale and diseconomies of scale.
Economies of Scale: As the firm increases production, average costs decrease due to factors like specialization, bulk purchasing, and efficient use of resources.
Diseconomies of Scale: Beyond a certain point, increasing production leads to rising average costs due to factors like managerial inefficiencies or overuse of resources.
In the long run, the firmβs cost structure is represented by the long-run average cost curve (LRAC), which is typically U-shaped. This curve is derived from various short-run average cost curves at different scales of production.
Diagrammatic Representation
Short-Run Cost Curves: These include the AFC, AVC, ATC, and MC curves. The ATC and AVC curves are typically U-shaped, and the MC curve intersects both at their minimum points.
Long-Run Average Cost Curve (LRAC): The LRAC is also U-shaped, showing economies and diseconomies of scale. It is tangent to the lowest points of a series of short-run average cost curves.
In summary, the traditional theory of cost explains how production costs change with output, emphasizing the distinction between fixed and variable costs in the short run, and economies of scale in the long run.
HOW TO GET OUT OF FINANCIAL CRUNCH
1. Assess Your Financial Situation
β’ List your income and expenses: Start by making a clear list of all your income sources and monthly expenses.
β’ Track your spending: Understand where your money is going, and identify areas where you can cut back.
2. Cut Unnecessary Expenses
β’ Prioritize needs over wants: Focus on essentials (housing, food, utilities), and reduce or eliminate non-essential spending.
β’ Negotiate bills: Call service providers (e.g., internet, insurance) and negotiate for better rates.
3. Create a Budget
β’ Develop a strict budget: Allocate your income wisely, ensuring youβre spending less than you earn.
β’ Stick to cash or debit: Avoid credit card use, as it can lead to more debt. Use only what you have.
4. Increase Your Income
β’ Side gigs or freelancing: Use your skills to generate extra income.
β’ Sell unwanted items: Sell items you no longer need, such as clothes, electronics, or furniture.
β’ Consider part-time work: If time allows, pick up a part-time job or gig to boost your cash flow.
5. Pay Off High-Interest Debt First
β’ Focus on high-interest debt: Pay off high-interest debts (credit cards, personal loans) first to reduce the burden.
β’ Consider consolidation: If you have multiple debts, consolidating them into a lower-interest loan may help manage repayments.
6. Emergency Fund
β’ Set up a small emergency fund: Even while in a financial crunch, set aside a small amount monthly for emergencies to avoid using credit cards.
7. Seek Financial Assistance or Advice
β’ Talk to a financial advisor: If your situation is complex, a financial advisor may provide strategies to improve it.
8. Avoid New Debt
β’ No new loans or credit card debt: Focus on paying off existing obligations without taking on more debt.
9. Stay Disciplined
β’ Set goals: Keep focused by setting short- and long-term financial goals.
β’ Review your progress regularly: Check your financial health weekly or monthly and adjust your plan if needed.
With a combination of disciplined budgeting, increasing income, reducing expenses, and managing debt, you can begin to work your way out of a financial crunch.
Thanks
.
HOW ECONOMICS AFFECTS TO OUR LIFE
Life is based on Scarcity principle always and Economics affects our lives in numerous ways, both directly and indirectly. Here are some key areas where economics plays a role:
1. Personal Finances
β’ Income and Employment: Economics helps shape the job market, influencing the availability of jobs, wages, and employment opportunities. Economic policies and conditions can affect job stability and the demand for certain skills or industries.
β’ Inflation and Cost of Living: Inflation, controlled by economic policies, affects the prices of goods and services. As inflation rises, the cost of living increases, impacting what individuals can afford and their overall financial well-being.
β’ Saving and Investing: Interest rates, which are part of economic policies set by central banks, affect the returns on savings and investments. Higher interest rates mean higher returns on savings but also higher borrowing costs.
2. Government Policies and Services
β’ Taxes: Government fiscal policies, such as taxes, are a key aspect of economics. The amount of tax individuals and businesses pay affects disposable income, public services, and economic incentives for spending and saving.
β’ Public Services: Economic decisions determine the amount of resources allocated to public services like education, healthcare, and infrastructure. Better economic management can lead to improved public services.
β’ Welfare and Unemployment Benefits: Economics informs policies on welfare programs and unemployment benefits, helping people during economic downturns by providing safety nets.
3. Consumer Behavior
β’ Prices and Demand: The principles of supply and demand, central to economics, determine the prices of everyday products. When demand exceeds supply, prices rise, and vice versa.
β’ Choices and Preferences: Economics shapes consumer behavior by analyzing how individuals make choices based on limited resources. This can influence personal decisions on what to buy, where to live, and how to allocate money.
4. Business and Entrepreneurship
β’ Market Competition: Economics drives competition between businesses, influencing product quality, pricing, and innovation. Market dynamics force companies to improve efficiency and offer better value to consumers.
β’ Startups and Investments: Economic conditions, such as interest rates and market growth, impact entrepreneurial ventures. In a thriving economy, more individuals are willing to start businesses and investors are more willing to take risks.
5. Global Trade and Economy
β’ Imports and Exports: Global economic policies affect international trade, influencing what goods and services are available, their prices, and the economic relationships between countries.
β’ Exchange Rates: Currency exchange rates, determined by economic factors, affect the cost of traveling abroad and the price of imported goods. A stronger currency makes imports cheaper but may hurt exports.
6. Long-Term Planning
β’ Economic Cycles: Economics helps predict and understand economic cycles (booms and recessions), allowing individuals, businesses, and governments to plan for the future. Recessions can lead to job losses and lower consumer spending, while booms encourage growth and investment.
β’ Sustainability and Resources: Economics also focuses on managing scarce resources efficiently. Decisions on how resources are used, both natural and financial, impact future generations and long-term sustainability.
In summary, economics plays a vital role in shaping various aspects of our personal lives, society, and the global market. Understanding economics helps individuals make informed decisions in their daily lives, plan for the future, and understand broader societal issues.
LAW OF DIMINISHING MARGINAL UTILITY
The law od diminishing marginal utility is given by Alfred Marshall . This topic relates the utility in to majorly three forms : Initial utility which is the satisfaction consumer derives with the consumption of any commodity at a given point of time . Secondly Marginal utility which is diminshing , zoro and sometimes negative even . Whenever a consumer consumes more and more units of a single commodity the marginal utility goes on diminshing . Another aspect is total utility which is the sum total of utility which consumer gets while the consumption of any commodity , total utility increases, maximum and starts decreasing .
Working strategy of unemployed white collared
Hi there , the unmployment rate increases due to excessive monopoly effect of few companies in india . The drastic ratio of unemployed youth is due to their unskilled bookish knowledge with no practical skill to be learnt with. Hyper rate is leading to depression in them . Letβs try to increase emplyment opportunities to them or make enterprenual skills in them , there should be proper export promotion activities and we should adopt chineses modal of development to enhance the opportunities of maximum exports as local agricultural and manufacturing industries have already boosted . The new strategy of export orientation must be launched to adjust the surplus labour by which economic development of the country will be done , thanks jatin
INTRODUCTION TO MICRO ECONOMICS
Hi all kindly check the vlog post for introduction to micro economics
Microeconomics in Detail
Microeconomics is a branch of economics that studies the behavior of individual economic agents, such as households, firms, and governments, and how their decisions affect the allocation of resources and the distribution of goods and services. It focuses on the interactions between buyers and sellers, the factors influencing supply and demand, and how prices are determined in markets.
Key Concepts in Microeconomics:
Demand and Supply:
Demand refers to the quantity of a good or service that consumers are willing and able to purchase at various prices. The law of demand states that as the price of a good rises, the quantity demanded typically falls, and vice versa.
Supply refers to the quantity of a good or service that producers are willing to sell at different price levels. The law of supply suggests that as prices increase, the quantity supplied typically increases as well.
The intersection of the demand and supply curves determines the market equilibrium price and quantity.
Elasticity:
Elasticity measures how responsive the quantity demanded or supplied is to changes in price or income.
Price elasticity of demand (PED) measures how much the quantity demanded responds to price changes. If demand is elastic, a small price change leads to a large change in quantity demanded.
Price elasticity of supply (PES) examines how the quantity supplied responds to changes in price.
Income elasticity looks at how demand for goods changes with consumer income.
Consumer Behavior and Utility:
Microeconomics explores how consumers make decisions based on their preferences and the concept of utilityβthe satisfaction or benefit derived from consuming goods or services. The Law of Diminishing Marginal Utility states that as a person consumes more of a good, the additional satisfaction (marginal utility) derived from each additional unit decreases.
Production and Costs:
Microeconomics also studies how firms produce goods and services and the associated costs. Firms aim to minimize production costs and maximize profit. Key cost concepts include:
Fixed costs: Costs that do not change with output levels, such as rent and salaries.
Variable costs: Costs that change with the level of production, like materials and labor.
Marginal cost: The additional cost incurred from producing one more unit of output.
Market Structures:
Microeconomics examines different market structures, including:
Perfect Competition: Many firms, identical products, and no barriers to entry.
Monopoly: One firm dominates the market with significant barriers to entry.
Oligopoly: A few large firms dominate the market.
Monopolistic Competition: Many firms offer similar but not identical products.
These structures impact pricing, competition, and efficiency within markets.
Market Failures and Government Intervention:
Microeconomics addresses situations where markets fail to efficiently allocate resources, leading to market failures. Common causes of market failure include externalities (e.g., pollution), public goods (e.g., national defense), and information asymmetry (e.g., when one party has more information than the other). In such cases, government intervention through regulation, taxation, or subsidies may be necessary to correct these failures.
Factor Markets:
Microeconomics also studies how the factors of production (land, labor, capital, and entrepreneurship) are allocated in markets. It looks at wage determination in labor markets, rent in land markets, and interest rates in capital markets.
Key Factors affecting Demand
Hi there , in this lecture we shall deal with factors affecting demand
The demand curve represents the relationship between the quantity of a good or service that consumers are willing to purchase and the price of that good or service. Various factors can shift the demand curve to the right (increase in demand) or to the left (decrease in demand). Here are the key factors affecting the demand curve:
1. Price of the Good or Service
β’ Law of Demand: There is an inverse relationship between price and quantity demanded, meaning as the price of a good increases, the quantity demanded generally decreases, and vice versa.
2. Income Levels
β’ Normal Goods: As consumer income increases, the demand for normal goods increases, shifting the demand curve to the right.
β’ Inferior Goods: As consumer income increases, the demand for inferior goods decreases, shifting the demand curve to the left.
3. Tastes and Preferences
β’ Changes in consumer preferences can increase or decrease the demand for certain goods. For example, a new fashion trend or health study can make a product more popular, increasing demand.
4. Prices of Related Goods
β’ Substitutes: If the price of a substitute good increases, the demand for the original good may increase, shifting the demand curve to the right.
β’ Complements: If the price of a complementary good increases, the demand for the original good may decrease, shifting the demand curve to the left.
5. Consumer Expectations
β’ Expectations about future prices or income can affect current demand. For instance, if consumers expect prices to rise in the future, they might buy more now, increasing current demand.
6. Population and Demographics
β’ An increase in the population or changes in demographics (e.g., age distribution) can increase the demand for certain goods, shifting the demand curve to the right.
7. Government Policies
β’ Taxes and Subsidies: A tax on a good can decrease demand, while a subsidy can increase demand.
β’ Regulations: Laws and regulations can either increase or decrease demand depending on their nature.
8. Seasonal Changes
β’ Certain goods have seasonal demand. For example, demand for winter clothing increases during the winter months, shifting the demand curve to the right.
9. Advertising and Marketing
β’ Effective advertising can increase consumer awareness and preference for a product, thereby increasing demand and shifting the demand curve to the right.
Each of these factors can independently or collectively cause shifts in the demand curve, altering the quantity demanded at any given price.
Thanks a lot
Dispersion : Quartile Deviation in Continuous Series
Quartile deviation is also known as the semi-interquartile range, is a measure of statistical dispersion. It indicates the spread of the middle 50% of a dataset. The quartile deviation is calculated using the first quartile (Q1) and the third quartile (Q3). The formula is:
Quartile Deviation=π3βπ1/2
Coefficient of Quartile Deviation = π3βπ1/π3+π1
β
Hereβs a step-by-step explanation:
Arrange Data: Organize the data set in ascending order.
Find Quartiles:
Q1 (First Quartile): The median of the lower half of the dataset (not including the median if the dataset has an odd number of observations).
Q3 (Third Quartile): The median of the upper half of the dataset (not including the median if the dataset has an odd number of observations).
Calculate Quartile Deviation: Subtract Q1 from Q3 and divide by 2.
The quartile deviation provides a robust measure of spread as it is not affected by extreme values or utliers. afterwards find coefficient of quartile deviation by formula QD = π3βπ1/π3+π1 you can watch the video for practical solution of this in various type of series like Individual Series , Discrete Series and Continuous Series. Here in this lecture you will find the Practical Solution in Continuous Series , kindly check the link here and do Subscribe to the channel :
Thanks a Lot
jatin
Dispersion : Quartile Deviation in Discrete Series
Quartile deviation is also known as the semi-interquartile range, is a measure of statistical dispersion. It indicates the spread of the middle 50% of a dataset. The quartile deviation is calculated using the first quartile (Q1) and the third quartile (Q3). The formula is:
Quartile Deviation=π3βπ1/2
Coefficient of Quartile Deviation = π3βπ1/π3+π1
β
Hereβs a step-by-step explanation:
Arrange Data: Organize the data set in ascending order.
Find Quartiles:
Q1 (First Quartile): The median of the lower half of the dataset (not including the median if the dataset has an odd number of observations).
Q3 (Third Quartile): The median of the upper half of the dataset (not including the median if the dataset has an odd number of observations).
Calculate Quartile Deviation: Subtract Q1 from Q3 and divide by 2.
The quartile deviation provides a robust measure of spread as it is not affected by extreme values or utliers. afterwards find coefficient of quartile deviation by formula QD = π3βπ1/π3+π1 you can watch the video for practical solution of this in various type of series like Individual Series , Discrete Series and Continuous Series. Here in this lecture you will find the Practical Solution in Discrete Series , kindly check the link here and do Subscribe to the channel :
Thanks a Lot
jatin
Statistical Analysis Practical Solutions for Various Topics
Multiplication of Matrices
Matrix multiplication is a binary operation that produces a new matrix from two matrices. Unlike addition and subtraction, the dimensions of the matrices involved in multiplication determine the possibility and the result of the operation. Matrix Multiplication involves two major conditions practically for finding AB where A assumes first matrix and B as Second matrix.
1.The no. of columns of first matrix should be equal to the no. of rows of second matrix only then multiplication is possible . if they are not equal then multiplication is not possible.
2. Multiply first row of first matrix with first column of second matrix then first row of first matrix with second column of second matrix then first row of first matrix with third column of second matrix then second row of first matrix with first column of second matrix and so on till the no. of row of first matrix and no. of column of second matrix.
Kindly check the link for practical solution of this method :
Matrix multiplication is a fundamental operation in linear algebra, widely used in various fields such as computer graphics, physics, economics, and statistics. Understanding its definition, properties, and application is crucial for effectively utilizing matrices in mathematical and applied contexts.
Addition & Subtraction of Matrices
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers in a matrix are called its elements or entries. A matrix with mmm rows and nnn columns is called an mΓnm \times nmΓn matrix, read as βm by n matrixβ.
Addition of Matrices : Matrix addition is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimensions, where each element of the resulting matrix is the sum of the corresponding elements of the input matrices.
Subtraction of Matrices : Matrix subtraction is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimensions, where each element of the resulting matrix is the difference of the corresponding elements of the input matrices.
Kindly check the link for practical implication of these methods :