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Question
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (A – B)T = AT – BT
Solution
We have,
A = `[(1, 2),(-1, 3)]`
B = `[(4, 0),(1, 5)]`
C = `[(2, 0),(1, -2)]`
And a = 4, b = –2
(A – B)T = `[(1 - 4, 2 - 0),(-1 - 1, 3 - 5)]^"T"`
= `[(-3, 2),(-2, -2)]^"T"`
= `[(-3, -2),(2, -2)]`
Now AT – BT = `[(1, -1),(2, 3)] - [(4, 1),(0, 5)]`
= `[(-3, -2),(2, -2)]`
= (A – B)T
Hence proved.
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