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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)T = AT – BT
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)T = `[(-3, 0),(2, -2)]` ...(1)
AT = `[(1, 1),(2, 3)]`
BT = `[(4, 1),(0, 5)]`
AT – BT = `[(1, 1),(2, 3)] - [(4, 1),(0, 5)]`
= `[(-3, 0),(2, -2)]` ...(2)
From (1) and (2) we get
(A – B)T = AT – BT
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