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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 10Matrices (up to 2×2) — Class 12 Business Mathematics and Basic Statistics, concept-first.

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter introduces matrices — a compact way of arranging numbers in rows and columns that businesses use every day to organise data such as sales figures, stock levels, or prices across products and branches.

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Q&A

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Concepts

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Unit weightage

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Key concepts

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Order and Types of Matrices

A matrix is a rectangular arrangement of numbers in rows and columns; if it has m rows and n columns its order is m×n (rows named first).

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Chapter contents

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1

Matrix Notation, Order, Rows and Columns

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter introduces matrices — a compact way of arranging numbers in rows and columns that businesses use every day to organise d…

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Types of Matrices

Matrices are classified into several standard types based on their order and the pattern of their elements. Recognising these types quickly is essential before moving on to matrix algebra.

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Addition and Subtraction of Matrices

Two matrices can be added or subtracted only if they are of the SAME order — this requirement is called being conformable for addition/subtraction.

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Scalar Multiplication of a Matrix

When a matrix is multiplied by an ordinary number (called a scalar, to distinguish it from a matrix), every SINGLE element of is multiplied by :

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Multiplication of Two Matrices (up to Order 2×2)

Two matrices and can be multiplied, in the order , only if the number of COLUMNS of equals the number of ROWS of .

Exercises

+Show 3 questions3 questions
  1. Q10Find the values of $a$, $b$, $c$ and $d$ if $\begin{pmatrix}2a&b-3\\c+1&4d\end{pmatrix} = \begin{pmatrix}8&5\\6&20\end{pmatrix}$.Free
  2. Q11If $A=\begin{pmatrix}4&-2\\2&6\end{pmatrix}$ and $B=\begin{pmatrix}-2&6\\4&-2\end{pmatrix}$, find the matrix $X$ such that $2X=A+B$.Preview
  3. Q12If $A=\begin{pmatrix}2&0\\1&3\end{pmatrix}$ and $I=\begin{pmatrix}1&0\\0&1\end{pmatrix}$ is the identity matrix of order 2, verify that $AI=…Preview

More questions

+Show 9 questions9 questions
  1. Example 1Write down the order of the matrix $A = \begin{pmatrix} 5 & -2 \\ 0 & 3 \end{pmatrix}$, and state the values of the elements $a_{12}$ and $a…Free
  2. Example 2For what values of $x$ and $y$ are the matrices $\begin{pmatrix} x+2 & 3 \\ 1 & y-4 \end{pmatrix}$ and $\begin{pmatrix} 7 & 3 \\ 1 & 2 \end{…Free
  3. Example 3Classify each of the following matrices as square, null, diagonal, scalar and/or identity, giving reasons: $P=\begin{pmatrix}4&0\\0&4\end{pm…Free
  4. Example 4If $A=\begin{pmatrix}3&-1\\2&5\end{pmatrix}$ and $B=\begin{pmatrix}-2&4\\1&-3\end{pmatrix}$, find (i) $A+B$ and (ii) $A-B$.Preview
  5. Example 5If $A=\begin{pmatrix}2&-3\\0&4\end{pmatrix}$, find $3A$ and $-2A$.Preview
  6. Example 6If $A=\begin{pmatrix}1&2\\3&-1\end{pmatrix}$ and $B=\begin{pmatrix}0&-1\\2&4\end{pmatrix}$, find $2A-3B$.Preview
  7. Example 7If $A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$ and $B=\begin{pmatrix}5&6\\7&8\end{pmatrix}$, find $AB$.Preview
  8. Example 8Using the same matrices $A=\begin{pmatrix}1&2\\3&4\end{pmatrix}$ and $B=\begin{pmatrix}5&6\\7&8\end{pmatrix}$ from the previous example, fin…Preview
  9. Example 9A company sells two products, P and Q, at two branches, Branch I and Branch II. The sales matrix for one month is $A=\begin{pmatrix}120&80\\…Preview