Let A be a 3 × 3 matrix with 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 arrow 2 R 2+5 R 3 on 2 A , then det ( B ) is equal to :

Question

Let A be a 3 × 3 matrix with 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 arrow 2 R 2+5 R 3 on 2 A , then det ( B ) is equal to : (A) 16 (B) 80 (C) 128 (D) 64

Tardigrade Admin · Accepted Answer

mid A| =4 ⇒ mid 2 A| =23 × 4=32 ∵ B is obtained by R 2 arrow 2 R 2+5 R 3 ⇒ | B |=2 × 32=64

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

16

80

128

64

$∣ A ∣ = 4$
$\Rightarrow∣ 2 A ∣ = 2^{3} \times 4 = 32$
$∵ B$ is obtained by $R_{2} \to 2 R_{2} + 5 R_{3}$
$\Rightarrow ∣ B ∣ = 2 \times 32 = 64$

Q. Let A be a 3×3 matrix with det (A)=4. Let Ri​ denote the ith row of A. If a matrix B is obtained by performing the operation R2​→2R2​+5R3​ on 2A, then det (B) is equal to :

16

80

128

64

∣A∣=4 ⇒∣2A∣=23×4=32 ∵B is obtained by R2​→2R2​+5R3​ ⇒∣B∣=2×32=64

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

$∣ A ∣ = 4$
$\Rightarrow∣ 2 A ∣ = 2^{3} \times 4 = 32$
$∵ B$ is obtained by $R_{2} \to 2 R_{2} + 5 R_{3}$
$\Rightarrow ∣ B ∣ = 2 \times 32 = 64$