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If a = [(3,1),(-1,2)] and I = [(1,0),(0,1)], Find A^2 - 5a + 7i - ICSE Class 10 - Mathematics

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Question

if A = `[(3,1),(-1,2)]` and `I = [(1,0),(0,1)]`, find `A^2 - 5A + 7I`

Solution

`A = [(3,1),(-1,2)], I = [(1,0),(0,1)]`

`A^2 = [(3,1),(-1,2)][(3,1),(-1,2)] = [(9-1, 3+2),(-3-2, -1+4)] = [(8,5),(-5,3)]`

`A^2 - 5A + 7I = [(8,5),(-5,3)] - 5[(3,1),(-1,2) ]+ 7[(1,0),(0,1)]`

`= [(8,5),(-5,3)] - [(15,5),(-5,10)] + [(7,0),(0,7)]`

`= [(-7,0),(0,-7)]+[(7,0),(0,7)]`

`= [(0,0),(0,0)]`

= 0

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Solution If a = [(3,1),(-1,2)] and I = [(1,0),(0,1)], Find A^2 - 5a + 7i Concept: Matrices Examples.
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