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Question
Given `A = [(1, 1),(-2, 0)]` and `B = [(2, -1),(1, 1)]`. Solve for matrix X:
3A – 2X = X – 2B
Solution
3A – 2X = X – 2B
–2x – X = –2B – 3A
–3x = –2B – 3A
3X = 3A + 2B
`X = A + 2/3B`
= `[(1, 1),(-2, 0)] + 2/3[(2, -1),(1, 1)]`
= `[(1, 1),(-2, 0)] + [((2 xx 2)/3, -2/3),(2/3, 2/3)]`
= `[(1, 1),(-2, 0)] + [(4/3, (-2)/3),(2/3, 2/3)]`
= `[(1 + 4/3, 1 - 2/3),(-2 + 2/3, 0 + 2/3)]`
= `[(7/3, 1/3),((-4)/3, 2/3)]`
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