Maharashtra State BoardHSC Commerce 12th Board Exam
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If A = [54-23] and B = [-134-1], then find CT, such that 3A – 2B + C = I, whre I is e unit matrix of order 2. - Mathematics and Statistics

Sum

If A = `[(5, 4),(-2, 3)]` and B = `[(-1, 3),(4, -1)]`, then find CT, such that 3A – 2B + C = I, whre I is e unit matrix of order 2.

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Solution

3A – 2B + C = I
∴ C = I + 2B – 3A

∴ C = `[(1, 0),(0, 1)] + 2[(-1, 3),(4, -1)] -3[(5, 4),(-2, 3)]`

= `[(1, 0),(0, 1)] +[(-2, 6),(8, -2)] - [(15, 12),(-6, 9)]`

= `[(1 - 2 - 15, 0 + 6 - 12),(0 + 8 + 6, 1 - 2 - 9)]`

∴ C = `[(-16, -6),(14, -10)]`

∴ C = `[(-16, 14),(-6, -10)]`.

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