Consider the matrix A = [[2, 0, 0],[1,1,-2],[1,-1, 0]]   (b) For which values of k is A-kI not invertible? These are the Eigenvalues of A.

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pramodpandey | College Teacher | (Level 3) Valedictorian

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A = [[2, 0, 0],[1,1,-2],[1,-1, 0]]


`A-kI `   is not invertible if  det(A-kI)=0 ,

Yes , k is the eigen value of matrix A.

`|A-kI|=(2-k)(-k+k^2-2)` =0

either  2-k=0







Thus if K=2,-1 then matrix A-kI will not invertible.

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