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If A= [(1,1,3),(5,2,6),(-2,-1,-3)] then ...

If `A= [(1,1,3),(5,2,6),(-2,-1,-3)]` then find `A^(14)+3A-2I`

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`[(1,1,3),(5,2,6),(-2,-1,-3)][(1,1,3),(5,2,6),(-2,-1,3)]= [(1+5-6, 1+2-3, 3+6-9),(5+10-12, 5+4-6,15+12-18),(-2-5+6, -2-2+3, -6-6+9)]`
`= [(0,0,0),(3,3,9),(-1,-1,-3)]`
`A^4 = A^2 xx A^2 = [(0,0,0),(3,3,9),(-1,-1,-3)][(0,0,0),(3,3,9),(-1,-1,-3)]`
`= [(0,0,0),(0,0,0),(0,0,0)]`
so, `A^14 + 3A-2I = 3[(1,1,3),(5,2,6),(-2,-1,-3)]- 2[(1,0,0),(0,1,0),(0,0,1)]`
`= [(3,3,9),(15,10,18),(-6,-3,-9)]-[(2,0,0),(0,2,0),(0,0,2)]`
`= [(1,3,9),(15,8,18),(-6,-3,-11)]`
Answer
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