If $A=\begin{pmatrix}2&-3\\0&4\end{pmatrix}$ and $B=\begin{pmatrix}1&2\\-1&3\end{pmatrix}$, find $2A-3B$.

If A= 2-3; 04 and B= 12; -13 , find 2A-3B.

Worked Examples · Example 4

A=\begin{pmatrix}2&-3\\0&4\end{pmatrix}

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Step 1 — Scalar multiply each matrix separately

2A=\begin{pmatrix}2(2)&2(-3)\\2(0)&2(4)\end{pmatrix}=\begin{pmatrix}4&-6\\0&8\end{pmatrix}

3B=\begin{pmatrix}3(1)&3(2)\\3(-1)&3(3)\end{pmatrix}=\begin{pmatrix}3&6\\-3&9\end{pmatrix}

Step 2 — Subtract element-by-element

$2A-3B=\begin{pmatrix}4-3&-6-6\\0-(-3)&8-9\end{pmatrix}=\begin{pmatrix}1&-12\\3&-1\end{pmatrix}$ …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2022Set ANNUAL1 markMCQ
$\begin{bmatrix} 2 \\ 4 \\ 6 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$
(a) $28$
(b) $[20]$
(c) $20$
(d) $[28]$
›Reveal solutionSolution

Inner product $2(1)+4(2)+6(3)=28$ , returned as a $1\times 1$ matrix $[28]$ .

The entries multiply pairwise and are added:

$2\times 1 + 4\times 2 + 6\times 3 = 2 + 8 + 18 = 28.$

…

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CBSE 2022Set ANNUAL1 markMCQ
$A = \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix}$
(a) $\begin{bmatrix} -6 & -9 \\ 3 & -12 \end{bmatrix}$
(b) $\begin{bmatrix} -6 & -9 \\ 1 & 4 \end{bmatrix}$
(c) $\begin{bmatrix} 2 & 3 \\ -3 & -12 \end{bmatrix}$
(d) $\begin{bmatrix} 6 & 9 \\ 3 & 12 \end{bmatrix}$
›Reveal solutionSolution

$-3A$ scales each entry by $-3$ ⇒ option (a).

Scalar multiplication of a matrix multiplies every element by the scalar: …

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CBSE 2022Set ANNUAL1 markMCQ
$\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} + \begin{bmatrix} -1 & -2 & 1 \\ -4 & -5 & 2 \end{bmatrix} + \begin{bmatrix} 9 & 8 & 7 \\ 6 & 5 & 4 \end{bmatrix}$
(a) $\begin{bmatrix} 9 & 8 & 7 \\ 6 & 5 & 4 \end{bmatrix}$
(b) $\begin{bmatrix} 9 & 8 & 11 \\ 6 & 5 & 12 \end{bmatrix}$
(c) $\begin{bmatrix} 11 & 12 & 11 \\ 14 & 15 & 12 \end{bmatrix}$
(d) $\begin{bmatrix} 0 & 0 & 7 \\ 0 & 0 & 4 \end{bmatrix}$
›Reveal solutionSolution

Element-wise addition ⇒ $\begin{bmatrix}9&8&11\\6&5&12\end{bmatrix}$ .

Matrices of the same order are added entry by entry:

$\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}+\begin{bmatrix}-1&-2&1\\-4&-5&2\end{bmatrix}+\begin{bmatrix}9&8&7\\6&5&4\end{bmatrix}.$

Row 1: $(1-1+9,\;2-2+8,\;3+1+7)=(9,\;8,\;11)$ . …

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←Previous questionExample 3 — If A= 6-3; 42 and B= -15; 3-4 , find (i) A+B and (ii) A-B.→Next questionExample 5 — If A= 123; 014 (order 2×3) and B= 20; 13; 02 (order 3×2), find AB.

Q.If $A=\begin{pmatrix}2&-3\\0&4\end{pmatrix}$ and $B=\begin{pmatrix}1&2\\-1&3\end{pmatrix}$ , find $2A-3B$ .

Concept understanding — Matrix Algebra: Addition, Subtraction and Multiplication

Q.If A=(2−304)A=\begin{pmatrix}2&-3\\0&4\end{pmatrix}A=(20​−34​) and B=(12−13)B=\begin{pmatrix}1&2\\-1&3\end{pmatrix}B=(1−1​23​), find 2A−3B2A-3B2A−3B.

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Q.If $A=\begin{pmatrix}2&-3\\0&4\end{pmatrix}$ and $B=\begin{pmatrix}1&2\\-1&3\end{pmatrix}$ , find $2A-3B$ .

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