Let A be a 3 × 3 matrix with det A = 4 . Let R i denote the i t h row of A . If a matrix B is obtained by performing the operation R 2 → 2 R 2 + 5 R 3 on 2 A , then det B is equal to :

Step-by-step solution

Let A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ⇒ 2 A = 2 a 11 2 a 12 2 a 13 2 a 21 2 a 22 2 a 23 2 a 31 2 a 32 2 a 33 R 2 → 2 R 2 + 5 R 3 B = 2 a 11 2 a 12 2 a 13 4 a 21 + 10 a 31 4 a 22 + 10 a 32 4 a 23 + 10 a 33 2 a 31 2 a 32 2 a 33 B = 2 a 11 2 a 12 2 a 13 4 a 21 + 10 a 31 4 a 22 + 10 a 32 4 a 23 + 10 a 33 2 a 31 2 a 32 2 a 33 B = 2 a 11 2 a 12 2 a 13 4 a 21 4 a 22 4 a 23 2 a 31 2 a 32 2 a 33 + 2 a 11 2 a 12 2 a 13 10 a 31 10 a 32 10 a 33 2 a 31 2 a 32 2 a 33 B = 2 × 4 × 2   a 11