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If a = [(3, A),(-4, 8)], B = [(C, 4),(-3, 0)], C = [(-1, 4),(3, B)] and 3a - 2c = 6b, Find the Values of A, B , C - ICSE Class 10 - Mathematics

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Question

If `A = [(3, a),(-4, 8)], B = [(c, 4),(-3, 0)], C = [(-1, 4),(3, b)]` and 3A - 2C = 6B, find the values of a, b , c.

Solution

3A - 2C = 6B

`3[(3, a),(-4, 8)] - 2[(-1, 4),(3, b)] = 6[(c, 4),(-3, 0)]`

`[(9, 3a),(-12, 24)] - [(-2, 8),(6, 2b)] = [(6c , 24),(-18, 0)]`

`[(11, 3a - 8),(-18, 24 - 2b)] = [(6c , 24),(-18, 0)]`

Comparing the corresponding elements we get

`3a - 8 = 24 => 3a = 32 => a = 32/3 = 10 2/3`

24 - 2b = 0 => 2b = 24 => b = 12

`11 = 6c => c = 11/6 = 1 5/6`

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Solution If a = [(3, A),(-4, 8)], B = [(C, 4),(-3, 0)], C = [(-1, 4),(3, B)] and 3a - 2c = 6b, Find the Values of A, B , C Concept: Matrices Examples.
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