If matrix $A = (2, 3, 4)$ and matrix $B = \begin{pmatrix} 5 \\ 6 \\ 7 \end{pmatrix}$, find $AB$.

If matrix A = (2, 3, 4) and matrix B = 5 \6 \7 , find AB.

Question 33 of 37

A = (2, 3, 4)

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$AB$ is a $1\times 1$ matrix equal to $56$ .

$A=\begin{pmatrix}2 & 3 & 4\end{pmatrix}$ is of order $1\times 3$ and $B=\begin{pmatrix}5\\6\\7\end{pmatrix}$ is of order $3\times 1$ . Since the inner dimensions match ( $3=3$ ), $AB$ exists and has order $1\times 1$ :

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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.If matrix $A = (2, 3, 4)$ and matrix $B = \begin{pmatrix} 5 \\ 6 \\ 7 \end{pmatrix}$ , find $AB$ .

Concept understanding — Matrix Algebra: Addition, Subtraction and Multiplication

Q.If matrix A=(2,3,4)A = (2, 3, 4)A=(2,3,4) and matrix B=(567)B = \begin{pmatrix} 5 \\ 6 \\ 7 \end{pmatrix}B=​567​​, find ABABAB.

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Q.If matrix $A = (2, 3, 4)$ and matrix $B = \begin{pmatrix} 5 \\ 6 \\ 7 \end{pmatrix}$ , find $AB$ .

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