Let A be a 3x3 matrix with that det(A) = 4,


Let $\mathrm{A}$ be a $3 \times 3$ matrix with $\operatorname{det}(\mathrm{A})=4$. Let $\mathrm{R}_{\mathrm{i}}$ denote the $\mathrm{i}^{\text {th }}$ row of $\mathrm{A}$. If a matrix $\mathrm{B}$ is obtained by performing the operation $\mathrm{R}_{2} \rightarrow 2 \mathrm{R}_{2}+5 \mathrm{R}_{3}$ on $2 \mathrm{~A}$, then $\operatorname{det}(\mathrm{B})$ is equal to :

  1. 16

  2.  80

  3. 128

  4. 64

Correct Option: , 4



$\Rightarrow|2 \mathrm{~A}|=2^{3} \times 4=32$

$\because \mathrm{B}$ is obtained by $\mathrm{R}_{2} \rightarrow 2 \mathrm{R}_{2}+5 \mathrm{R}_{3}$

$\Rightarrow|B|=2 \times 32=64$

option (4)

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