If A = 2 3 \-1 4 , then -3A is equal to : (a) -6 -9 \3 -12 (b) -6 -9 \1 4 (c) 2 3 \-3 -12 (d) 6 9 \3 12

Question 25 of 37

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}

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$-3A$ 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
$\begin{bmatrix} 2 \\ 4 \\ 6 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \end{bmatrix}$
(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.If $A = \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix}$ , then $-3A$ is equal to :

Concept understanding — Matrix Algebra: Addition, Subtraction and Multiplication

Q.If A=[23−14]A = \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix}A=[2−1​34​], then −3A-3A−3A is equal to :

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Q.If $A = \begin{bmatrix} 2 & 3 \\ -1 & 4 \end{bmatrix}$ , then $-3A$ is equal to :

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