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Question

If A= 31-12 and I=1001, then find λ so that A2 = 5A + λI.

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Solution

Given: A=31-12Now,A2=AAA2=31-1231-12A2=9-13+2-3-2-1+4A2=85-53A2=5A+λI85-53=531-12+λ100185-53=155-510+λ00λ85-53=15+λ5+0-5+010+λ85-53=15+λ5-510+λThe corresponding elements of two equal matrices are equal. 8=15+λ 8-15=λ -7=λ λ=-7

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