For the matrices A and B of Q1, find 2A-3B.

Exercise: Matrix Addition and Scalar ... · Q15

A

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$2A=\begin{bmatrix}4&-2\\0&6\end{bmatrix}$ and $3B=\begin{bmatrix}3&12\\-6&15\end{bmatrix}$ . Subtracting entrywise: $(1,1)$ : $4-3=1$ ; $(1,2)$ : $-2-12=-14$ ; $(2,1)$ : $0-(-6)=6$ ; $(2,2)$ : $6-15=-9$ . So $2A-3B=\begin{bmatrix}1&-14\\6&-9\end{bmatrix}$ . [!ANSWER] $2A-3B=\begin{bmatrix}1&-14\\6&-9\end{bmatrix}$ .

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

CBSE 2026Set SEM31 markMCQ
$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$
(i) $A + A^T$ ;
(ii) $(A + B)^T$ ;
(iii) $(AB)^T$ ;
(iv) $B + B^T$ . Right column:
(a) $\begin{bmatrix} -2 & -1 \\ -1 & 0 \end{bmatrix}$ ;
(b) $\begin{bmatrix} 2 & 5 \\ 5 & 8 \end{bmatrix}$ ;
(c) $\begin{bmatrix} 0 & 1 \\ 3 & 4 \end{bmatrix}$ ;
(d) $\begin{bmatrix} -5 & -11 \\ 1 & 3 \end{bmatrix}$ .
(a) (i)-(a), (ii)-(c), (iii)-(d), (iv)-(b)
(b) (i)-(b), (ii)-(c), (iii)-(a), (iv)-(d)
(c) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a)
(d) (i)-(b), (ii)-(d), (iii)-(c), (iv)-(a)
›Reveal solutionSolution
Compute each of the four matrices and match; the correct assignment is (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a).

Matrix operations and the transpose rules $(A+B)^T=A^T+B^T$ , $(AB)^T=B^TA^T$ are exactly the CBSE/NCERT Class 12 matrices topics tested here.

$A+A^T = \begin{bmatrix}1&2\\3&4\end{bmatrix}+\begin{bmatrix}1&3\\2&4\end{bmatrix} = \begin{bmatrix}2&5\\5&8\end{bmatrix}$ — matches (b).

$A+B = \begin{bmatrix}0&3\\1&4\end{bmatrix}$ , so $(A+B)^T = \begin{bmatrix}0&1\\3&4\end{bmatrix}$ — matches (c).

$AB = \begin{bmatrix}1&2\\3&4\end{bmatrix}\begin{bmatrix}-1&1\\-2&0\end{bmatrix} = \begin{bmatrix}-5&1\\-11&3\end{bmatrix}$ , so $(AB)^T = \begin{bmatrix}-5&-11\\1&3\end{bmatrix}$ — matches (d).

$B+B^T = \begin{bmatrix}-1&1\\-2&0\end{bmatrix}+\begin{bmatrix}-1&-2\\1&0\end{bmatrix} = \begin{bmatrix}-2&-1\\-1&0\end{bmatrix}$ — matches (a).

✓Final answer
$(i)-(b), (ii)-(c), (iii)-(d), (iv)-(a) — option (c).$

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Q.For the matrices $A$ and $B$ of Q1, find $2A-3B$ .

Concept understanding — Matrix Addition and Scalar Multiplication

Q.For the matrices AAA and BBB of Q1, find 2A−3B2A-3B2A−3B.

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Q.For the matrices $A$ and $B$ of Q1, find $2A-3B$ .

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