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Question
Given matrix B =`[(1,1), (8,3)]` Find the matrix X if, X = B2 - 4B. Hence, solve for a and b given X`[(a), (b)] = [(5), (50)]`
Solution
`B^2 = B xx B = [(1,1), (8,3)][(1,1), (8,3)] = [(1xx1+1xx8,1xx1+1xx3), (8xx1+3xx8,8xx1+3xx3)] = [(9,4), (32,17)]`
4B = 4`[(1,1), (8,3)] = [(4,4), (32,12)]`
Given : `X = B^2 - 4B`
`=> X = [(9,4), (32,17)] - [(4,4), (32,12)] = [(5,0), (0,5)]`
To find: a and b
X`[(a), (b)] = [(5), (50)]` ........given
`=> [(5,0), (0,5)][(a), (b)] = [(5), (50)]`
`=> [(5a), (5b)] = [(5), (50)]`
`=> 5[(a), (b)] = 5[(1), (10)]`
`=> a = 1 and b = 10
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