Let \(A = [a_{ij}]\) be a matrix of order \(2 \times 3\) whose elements are given by \(a_{ij} = 3i - 2j\).
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | \(a_{12}\) | (I) | 0 |
| (B) | \(a_{21}\) | (II) | 3 |
| (C) | \(a_{23}\) | (III) | \(-1\) |
| (D) | \(a_{11} + a_{22}\) | (IV) | 4 |
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)-(I), (D)-(II)
In \(a_{ij}\), the first suffix i is the row number and the second suffix j is the column number. Each element is found by putting these values in \(3i - 2j\).
(A) \(a_{12}\)
This matches (III) \(-1\).
\(a_{12} = 3(1) - 2(2) = -1\)
(B) \(a_{21}\)
This matches (IV) 4.
\(a_{21} = 3(2) - 2(1) = 4\)
(C) \(a_{23}\)
This matches (I) 0.
\(a_{23} = 3(2) - 2(3) = 0\)
(D) \(a_{11} + a_{22}\)
This matches (II) 3.
\(a_{11} = 3(1) - 2(1) = 1\)
\(a_{22} = 3(2) - 2(2) = 2\)
\(a_{11} + a_{22} = 1 + 2 = 3\)