A= $⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦$ .
B is matrix obtained by subtracting $4 t i m e s 1^{s t} r o w f r o m 2^{n d} r o w$ of A. Find matrix B

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 3 & 6 0 & 6 & 12 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 7 & 0 & 0 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & 1 & 2 3 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦

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Solution

The correct option is C $⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦$
Given $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦$
$\Rightarrow R_{2} \to R_{2} - 4 R_{1}$ (for matrix B)
$\Rightarrow B - ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 - 4 (1) & 5 - 4 (2) & 6 - 4 (3) 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 0 & - 3 & - 6 7 & 8 & 9 \end{matrix} ⎤ ⎥ ⎦$
Option D is correct

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