If a_ij = 1/2(3i - 2j) and A = [a_ij]_2 × 2 , then A is equal to: - Mathematics MCQ Mathematics Mock Test - 2 2026 | ExamTest.live

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If a_{ij} = \frac{1}{2} (3 i - 2 j) and A = [a_{ij}]_{2 \times 2}, then A is equal to:

Solution & Step-by-step Explanation

A 2 \times 2 matrix has the form: A = [a_{11} a_{21} a_{12} a_{22}] Calculate each element using a_{ij} = \frac{1}{2} (3 i - 2 j) : a_{11} = \frac{1}{2} (3 (1) - 2 (1)) = \frac{1}{2} (1) = 1/2 a_{12} = \frac{1}{2} (3 (1) - 2 (2)) = \frac{1}{2} (3 - 4) = - 1/2 a_{21} = \frac{1}{2} (3 (2) - 2 (1)) = \frac{1}{2} (6 - 2) = 4/2 = 2 a_{22} = \frac{1}{2} (3 (2) - 2 (2)) = \frac{1}{2} (6 - 4) = 2/2 = 1 The matrix is: A = [1/2 2 - 1/2 1]

Try it yourself before checking the explanation above.

If a_{ij} = \frac{1}{2} (3 i - 2 j) and A = [a_{ij}]_{2 \times 2}, then A is equal to:

[1/2 - 1/2 21]

[1/2 2 - 1/2 1]

[2 1/2 2 - 1/2]

None of these

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