Let A=a_ij and B=b_ij be two 3×3 real matrices such that b_ij=3^(i+j-2)a_ij , where i,j=1,2,3 . If the determinant of B is 81 , then determinant of A…

Question

Let A=a_ij and B=b_ij be two 3×3 real matrices such that b_ij=3^(i+j-2)a_ij , where i,j=1,2,3 . If the determinant of B is 81 , then determinant of A i s

MARKS Content Team · Accepted Answer

Correct answer: (D) 1/9. B= b_11 b_12 b_13 b_21 b_22 b_23 b_31 b_32 b_33 = 3^0a_11 3^1a_12 3^2a_13 3^1a_21 3^2a_22 3^3a_23 3^2a_31 3^3a_32 3^4a_33 ⇒81=3^3∙3∙3^2A⇒3^4=3^6A⇒A=1/9

Let $A = [a_{i j}]$ and $B = [b_{i j}]$ be two $3 \times 3$ real matrices such that $b_{i j} = {(3)}^{(i + j - 2)} a_{i j}$ , where $i, j = 1,2, 3$ . If the determinant of $B$ is $81$ , then determinant of $A$ i s

Solution

Relevant Questions

Let A=aij and B=bij be two 3×3 real matrices such that bij=3i+j-2aij , where i,j=1,2,3 . If the determinant of B is 81 , then determinant of A i s

Solution

Relevant Questions

Let $A = [a_{i j}]$ and $B = [b_{i j}]$ be two $3 \times 3$ real matrices such that $b_{i j} = {(3)}^{(i + j - 2)} a_{i j}$ , where $i, j = 1,2, 3$ . If the determinant of $B$ is $81$ , then determinant of $A$ i s