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