Let A be a 3×3 matrix with det(A) = 4 | Matrices JEE Main 2021

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JEE MAIN 2021

25-02-2021 S12

Question

Let $A$ be a $3 \times 3$ matrix with $\operatorname{det}(A)=4$. Let $R_i$ denote the ith row of $A$. If a matrix $B$ is obtained by performing the operation $\mathrm{R}_2 \rightarrow 2 \mathrm{R}_2+5 \mathrm{R}_3$ on 2 A , then $\operatorname{det}(B)$ is equal to :

Select the correct option:

A

16

B

80

C

128

D

64

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & |A|=4 \\ & \Rightarrow \quad|2 A|=2^3 \times 4=32 \\ & \square \quad B \text { is obtained by } R_2 \rightarrow 2 R_2+5 R_3 \\ & \Rightarrow \quad|B|=2 \times 32=64\end{aligned}$

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