Match List-I (a kind of square matrix of order 4) with List-II (the least number of its elements that must be known to write the whole matrix).
| List-I | List-II | ||
|---|---|---|---|
| (A) | Symmetric matrix | (I) | 1 |
| (B) | Skew-symmetric matrix | (II) | 4 |
| (C) | Diagonal matrix | (III) | 6 |
| (D) | Scalar matrix | (IV) | 10 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
A square matrix of order 4 has 16 elements: 4 on the main diagonal and 12 off it, of which 6 lie above the diagonal and 6 below.
(A) Symmetric matrix
This matches (IV) 10.
\(a_{ji} = a_{ij}\): the 6 elements below the diagonal copy those above, so \(4 + 6 = 10\) are needed
(B) Skew-symmetric matrix
This matches (III) 6.
\(a_{ii} = -a_{ii}\) gives diagonal elements 0, and \(a_{ji} = -a_{ij}\): only the 6 above the diagonal are needed
(C) Diagonal matrix
This matches (II) 4.
All 12 off-diagonal elements are 0; only the 4 diagonal elements are needed
(D) Scalar matrix
This matches (I) 1.
It is kI, so the single common diagonal element k is enough