Match List - I with List - II.
| List - I | List - II | ||
| (A) | Null matrix | (I) | \(\begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}\) |
| (B) | Scalar matrix | (II) | \(\begin{bmatrix} 0 & -5 & -3 \\ 5 & 0 & -2 \\ 3 & 2 & 0 \end{bmatrix}\) |
| (C) | Skew-symmetric matrix | (III) | \(\begin{bmatrix} 1 & 7 & 2 \\ 7 & 5 & 3 \\ 2 & 3 & 6 \end{bmatrix}\) |
| (D) | Symmetric matrix | (IV) | both symmetric and skew-symmetric |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
(A) Null matrix
This matches (IV) both symmetric and skew-symmetric.
A matrix with A' = A and A' = −A has A = −A, so every entry is 0: it is the null matrix.
(B) Scalar matrix
This matches (I).
It is a diagonal matrix with all diagonal entries equal (5), that is 5I.
(C) Skew-symmetric matrix
This matches (II).
The diagonal entries are 0 and \(a_{ji} = -a_{ij}\) (for example 5 and −5, 3 and −3, 2 and −2).
(D) Symmetric matrix
This matches (III).
\(a_{ji} = a_{ij}\) for every pair (7 and 7, 2 and 2, 3 and 3).