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Question
If A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]` and I is the identity matric of the same order and At is the transpose of matrix A, find At.B + BI.
Solution
Given A = `[(2, 5),(1, 3)]`, B = `[(4, -2),(-1, 3)]`
At = `[(2, 1),(5, 3)]`
At.B + BI = `[(2, 1),(5, 3)][(4, -2),(-1, 3)] + [(4, -2),(-1, 3)][(1, 0),(0, 1)]`
= `[(8 - 1, -4 + 3),(20 - 3, -10 + 9)] + [(4 + 0, 0 - 2),(-1 + 0, 0 + 3)]`
= `[(7, -1),(17, -1)] + [(4, -2),(-1, 3)]`
= `[(7 + 4, -1 - 2),(17 - 1, -1 + 3)]`
= `[(11, -3),(16, 2)]`
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