Match List-I with List-II
| List-I | List-II | ||
| (A) | \( \begin{bmatrix} 1 & -2 & 0\\ 0 & 4 & 3\\ 0 & 0 & 0\end{bmatrix} \) | (I) | Symmetric matrix |
| (B) | \( \begin{bmatrix} 5 & 0 & 0\\ 3 & 0 & 0\\ 1 & -2 & 4\end{bmatrix} \) | (II) | Upper triangular matrix |
| (C) | \( \begin{bmatrix} 0 & 1 & 2\\ 1 & 3 & -4\\ 2 & -4 & 5\end{bmatrix} \) | (III) | Diagonal matrix |
| (D) | \( \begin{bmatrix} 3 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 0\end{bmatrix} \) | (IV) | Lower triangular matrix |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
(A) All entries below the diagonal are 0, so it is an upper triangular matrix. This matches (II).
(B) All entries above the diagonal are 0, so it is a lower triangular matrix. This matches (IV).
(C) \( a_{ij}=a_{ji} \) for all i, j, so it is a symmetric matrix. This matches (I).
(D) Only the diagonal entries are non-zero, so it is a diagonal matrix. This matches (III).
So the matching is (A) - (II), (B) - (IV), (C) - (I), (D) - (III).
Note: Some List-I items fit more than one List-II entry. The diagonal matrix in (D) is also symmetric, upper triangular and lower triangular, so (D) fits (I), (II), (III) and (IV). The question can still be solved because (A) fits only (II), (B) fits only (IV) and (C) fits only (I), and Option (2) is the only option containing (A)-(II), (B)-(IV) and (C)-(I).