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Question
Let A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]` Show that (A – B)C = AC – BC
Solution
A = `[(1, 2),(1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, 2)]`
A – B = `[(1, 2),(1, 3)] - [(4, 0),(1, 5)]`
= `[(-3, 2),(0, -2)]`
(A – B)C = `[(-3, 2),(0, -2)] xx [(2, 0),(1, 2)]`
= `[(-6 + 2, 0 + 4),(0 - 2, 0 - 4)]`
= `[(-4, 4),(-2, -4)]` ...(1)
AC = `[(1, 2),(1, 3)] xx [(2, 0),(1, 2)]`
= `[(2 + 2, 0 + 4),(2 + 3, 0 + 6)]`
= `[(4, 4),(5, 6)]`
BC = `[(4, 0),(1, 5)] xx [(2, 0),(1, 2)]`
= `[(8 + 0, 0 + 0),(2 + 5, 0 + 10)]`
= `[(8, 0),(7, 10)]`
AC – BC = `[(4, 4),(5, 6)] - [(8, 0),(7, 10)]`
= `[(-4, 4),(-2, -4)]` ...(2)
From (1) and (2) we get
(A – B)C = AC – BC
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