Match List I with List II
| List I | List II | ||
| A | Number of possible matrices of order $3×2$ using 8 or 3 is | I | 9 |
| B | Sum of all diagonal elements of $\begin{bmatrix}5 & 3\\1 & -3\end{bmatrix}$ | II | 64 |
| C | If $\begin{bmatrix}a-b & 11\\-5 & a^2-b^2\end{bmatrix}=\begin{bmatrix}3&11\\-5&27\end{bmatrix}$ then $\frac{(ab)}{2}$ is | III | 0 |
| D | Sum of all non-diagonal elements of skew-symmetric matrix of order 3×3 | IV | 2 |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-II, B-IV, C-I, D-III
(A) No. of possible matrix is, $2^6=64$
(B) $\begin{bmatrix}5 & 3\\1 & -3\end{bmatrix}$ ⇒ Sum of Diagonal elements = $5+(-3)=2$
(C) $\begin{bmatrix}a-b & 11\\-5 & a^2-b^2\end{bmatrix}=\begin{bmatrix}3&11\\-5&27\end{bmatrix}$ then $\frac{(ab)}{2}$
$⇒a-b=3$ ...(1)
$⇒a^2-b^2=27$ ...(2)
From (1) and (2),
$a+b=9$ ...(3)
Adding (1) and (3),
$2a=12$
$a=6⇒b=3$
$∴\frac{(ab)}{2}=\frac{6×3}{2}=9$
(D) All the diagonal elements of skew symmetric matrices are zero.
∴ Sum = 0