(f) If $A = \begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}$, $B = \begin{pmatrix} 1 & -3 \\ 2 & 4 \end{pmatrix}$, find $3A + 2B$.

(f) If A = 2 1 \5 2 , B = 1 -3 \2 4 , find 3A + 2B.

Question 18 of 37

A = \begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}

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$3A + 2B = \begin{pmatrix} 8 & -3 \\ 19 & 14 \end{pmatrix}$ .

First multiply each matrix by its scalar:

$3A = 3\begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix} = \begin{pmatrix} 6 & 3 \\ 15 & 6 \end{pmatrix}, \qquad 2B = 2\begin{pmatrix} 1 & -3 \\ 2 & 4 \end{pmatrix} = \begin{pmatrix} 2 & -6 \\ 4 & 8 \end{pmatrix}.$

Now add the corresponding elements: …

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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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Q.(f) If $A = \begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}$ , $B = \begin{pmatrix} 1 & -3 \\ 2 & 4 \end{pmatrix}$ , find $3A + 2B$ .

Concept understanding — Matrix Algebra: Addition, Subtraction and Multiplication

Q.(f) If A=(2152)A = \begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}A=(25​12​), B=(1−324)B = \begin{pmatrix} 1 & -3 \\ 2 & 4 \end{pmatrix}B=(12​−34​), find 3A+2B3A + 2B3A+2B.

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Q.(f) If $A = \begin{pmatrix} 2 & 1 \\ 5 & 2 \end{pmatrix}$ , $B = \begin{pmatrix} 1 & -3 \\ 2 & 4 \end{pmatrix}$ , find $3A + 2B$ .

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