Q.

Let A be a 3×3 matrix with detA=4 . Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation  on 2A, then det (B) is equal toLet A be a  matrix with  . Let  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

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a

64

b

16

c

128

d

80

answer is A.

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Detailed Solution

Given the matrix A is a square matrix of order 3 and having the determinant 4. Suppose that A=a1a2a3b1b2b3c1c2c3    and 2A=2a12a22a32b12b22b32c12c22c3   Perform the operation R2→2R2 +5R3 on the matrix 2AThe equivalent matrix is 2A=2a12a22a34b1+10c14b2+10c24b3+10c32c12c22c3   Hence, 2A=2a12a22a34b14b24b32c12c22c3+0         · Two rows are equal in the other matrix, so it is zero=242A=164=64Det (B) is 64.
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