# Find matrices A and B, if 2A – B = [6-60-421] and A – 2B = [328-21-7]. - Mathematics and Statistics

Sum

Find matrices A and B, if 2A – B = [(6, -6, 0),(-4, 2, 1)] and A – 2B = [(3, 2, 8),(-2, 1, -7)].

#### Solution

Given equations are

2A – B = [(6, -6, 0),(-4, 2, 1)]           ...(i)

and A – 2B = [(3, 2, 8),(-2, 1, -7)]    ...(ii)

By (i) – (ii) x 2, we get

3B = [(6, -6, 0),(-4, 2, 1)] - 2[(3, 2, 8),(-2, 1, -7)]

= [(6, -6, 0),(-4, 2, 1)] - [(6, 4, 16),(-4, 2, -14)]

= [(6 - 6, -6 - 4,  0 - 16),(-4 + 4, 2 - 2, 1 + 14)]

∴ 3B = [(0, -10, -16),(0, 0, 15)]

∴ B = (1)/(3)[(0, -10, -16),(0, 0, 15)]

∴ B = [(0, (-10)/3, (-16)/3),(0, 0, 5)]

By (i) x 2 –  (ii), we get

3A = 2[(6, -6, 0),(-4, 2, 1)] - [(3, 2, 8),(-2, 1, -7)]

= [(12, -12, 0),(-8, 4, 2)] - [(3,  2, 8),(-2, 1, -7)]

= [(12 - 3, -12 - 2, 0 - 8),(-8 + 2 , 4  - 1, 2 + 7)]

∴ 3A = [(9, -14, -8),(-6, 3, 9)]

∴ A = (1)/(3)[(9, 14, -8),(-6, 3, 9)]

∴ A = [(3, (-14)/3, (-8)/3),(-2, 1, 3)].

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