Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| A. | A = \( \begin{bmatrix}3 & 5\\5 & 2\end{bmatrix} \) | I. | Scalar matrix |
| B. | A = \( \begin{bmatrix}0 & -2\\2 & 0\end{bmatrix} \) | II. | Upper triangular matrix |
| C. | A = \( \begin{bmatrix}5 & 3\\0 & 4\end{bmatrix} \) | III. | Symmetric matrix |
| D. | A = \( \begin{bmatrix}3 & 0\\0 & 3\end{bmatrix} \) | IV. | Skew-symmetric matrix |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-III, B-IV, C-II, D-I
(A) A = \( \begin{bmatrix}3 & 5\\5 & 2\end{bmatrix} \)
This matches III. Symmetric matrix. The entries opposite the diagonal are equal (5 and 5), so \( A^T=A \).
(B) A = \( \begin{bmatrix}0 & -2\\2 & 0\end{bmatrix} \)
This matches IV. Skew-symmetric matrix. The diagonal entries are 0 and the (1, 2) and (2, 1) entries are negatives of each other, so \( A^T=-A \).
(C) A = \( \begin{bmatrix}5 & 3\\0 & 4\end{bmatrix} \)
This matches II. Upper triangular matrix. The only entry below the diagonal is 0.
(D) A = \( \begin{bmatrix}3 & 0\\0 & 3\end{bmatrix} \)
This matches I. Scalar matrix. It is a diagonal matrix with equal diagonal entries (3I).
So the matching is A-III, B-IV, C-II, D-I.