Let A=aij_(3×3) and B=b_ij3×3, where b_ij=(a_ij+a_ji)/2 ∀i,j. Number of such matrices A whose elements are selected from the set 0,1,2,3 such that…

Question

Let A=aij_(3×3) and B=b_ij3×3, where b_ij=(a_ij+a_ji)/2 ∀i,j. Number of such matrices A whose elements are selected from the set 0,1,2,3 such that A=B, are

MARKS Content Team · Accepted Answer

Correct answer: (B) 2^12. A= a_11 a_12 a_13 a_21 a_22 a_23 a_31 a_32 a_33 and B= b_11 b_12 b_13 b_21 b_22 b_23 b_31 b_32 b_33 ∵A=B⇒a_ij=b_ij=(a_ij+a_ji)/2 ⇒a_ij=a_ji ⇒A is a symmetric matrix Hence, the number of such matrix=4×4×4×4×4×4=4^6=2^12

Let $A = {(a_{i j})}_{3 \times 3}$ and $B = {(b_{i j})}_{3 \times 3}$ , where $b_{i j} = \frac{a_{i j} + a_{j i}}{2} \forall i, j .$ Number of such matrices $A$ whose elements are selected from the set $\{0, 1,2, 3\}$ such that $A = B$ , are

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More Matrices Questions

Let A=aij3×3 and B=bij3×3, where bij=aij+aji2 ∀i,j. Number of such matrices A whose elements are selected from the set 0,1,2,3 such that A=B, are

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More Matrices Questions

Let $A = {(a_{i j})}_{3 \times 3}$ and $B = {(b_{i j})}_{3 \times 3}$ , where $b_{i j} = \frac{a_{i j} + a_{j i}}{2} \forall i, j .$ Number of such matrices $A$ whose elements are selected from the set $\{0, 1,2, 3\}$ such that $A = B$ , are