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Question

If A=2312 and I=1001, then find λ, μ so that A2 = λA + μI

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Solution

Given: A=2312Now,A2=AAA2=23122312A2=4+36+62+23+4A2=71247A2=λA+μI71247=λ2312+μ100171247=2λ3λλ2λ+μ00μ71247=2λ+μ3λ+0λ+02λ+μ71247=2λ+μ3λλ2λ+μThe corresponding elements of two equal matrices are equal. 7=2λ+μ ...1 12=3λλ=123=4Putting the value of λ in eq. 1, we get 7=24+μ7-8=μ μ=-1

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