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