Let A be a 3 × 3 matrix with operatorname{det}( A )=4 . Let R _{ i } denote i ^{text {th }} r

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3 and 4 .Determinants and Matrices

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

A

$16$

B

$80$

C

$128$

D

$64$

(JEE MAIN-2021)

Solution

$\mid A \mid =4$

$\Rightarrow \mid 2 A \mid =2^{3} \times 4=32$

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

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

Standard 12

Mathematics

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