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Question
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A – B)T = AT – BT
Solution
AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`
A – B = `[(4, - 1, 2),(5, 0, 3)] - [(2, -1, 1),(7, 5, -2)]`
= `[(4 - 2, -1 + 1, 2 - 1),(5 - 7, 0 - 5, 3 + 2)]`
A – B = `[(2, 0, 1),(-2, -5, -5)]`
(A – B)T = `[(2, 2),(0, -5),(1, 5)]` .......(4)
AT – BT = `[(4, 5),(-1, 0),(2, 3)] - [(2, 7),(-1, 5),(1, -2)]`
= `[(4 - 2, 5 -7),(-1 + 1, 0 - 5),(2 - 1, 3 + 2)]`
AT – BT = `[(2, 2),(0, -5),(1, 5)]` ......(5)
From equation (1) and (2)
(A – B)T = AT – BT
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