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Question
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.
Solution
3A – 5BT = `3[(2, -3),(3, -2),(-1, 4)] -[(-3, 2),(4, -1),(1, -3)]`
= `[(6, -),(9, -6),(-3, 12)] - [(-15, 10),(20, -5),(5, -15)]`
= `[(6 + 15, -9 - 10),(9 - 20, -6 + 5),(-3 - 5, 12 + 15)]`
∴ 3A – 5BT = `[(21, -19),(-11, -1),(-8, 27)]`
∴ (3A – 5BT)T = `[(21, -11, -8),(-19, -1, 27)]` ...(i)
3AT – 5B = `3[(2, 3, -1),(-3, -2, 4)] - 5[(-3, 4, 1),(2, -1, -3)]`
= `[(6, 9, -3),(-9, 16, 12)] - [(-15, 20, 5),(10, -5, -15)]`
= `[(6 + 15, 9 - 20, -3 - 5),(-9 - 10, -6 + 5, 12 + 15)]`
= `[(2, -11, -8),(-19, -1, 27)]` ...(ii)
From (i) and (ii), we get
(3A – 5BT)T = 3AT – 5B.
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