1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A be 3 × 3 matrix given by A=[ai j] and B be a column vector such that B⊤ A B is a null matrix for every column vector B. If C=A-A⊤ and a13=1, a23=-5, a21=15, then find the value of operatornamedet( operatornameadj A)+ operatornamedet( operatornameadj C). ,br/>[Note: adj M denotes the adjoint of a square matrix M.]

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Q. Let $A$ be $3 \times 3$ matrix given by $A=\left[a_{i j}\right]$ and $B$ be a column vector such that $B^{\top} A B$ is a null matrix for every column vector $B$. If $C=A-A^{\top}$ and $a_{13}=1, a_{23}=-5, a_{21}=15$, then find the value of $\operatorname{det}(\operatorname{adj} A)+\operatorname{det}(\operatorname{adj} C)$. ,br/>[Note : adj $M$ denotes the adjoint of a square matrix $M$.]

Matrices

Solution:

Correct answer is '0'