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If a = [(2,5),(1,3)], B = [(4,-2),(-1,3)]` and I = I is the Identity Matrix of the Same Order and at is the Transpose of Matrix A, Find At.B + Bi. - Mathematics

if A = [(2,5),(1,3)], B = [(4,-2),(-1,3)]` and I =  I is the identity matrix of the same order and At is the transpose of matrix A, find At.B + BI.

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Solution

Given `A = [(2,5),(1,3)], B = [(4, -2),(-1,3)]`

`A^t = [(2,1),(5,3)]`

`A^t.B + B.I = [(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)]`

Concept: Matrices Examples
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