Q:

For matrix A =

0

For matrix

the characteristic polynomial of A is pA (x) =(x + 2)(x 2)2(x 4). Find the eigenvalues and corresponding eigenspaces of A.

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Since we are given that the characteristic polynomial of A is pA (x) = (x + 2)(x 2)2(x 4), we see that the eigenvalues are λ = 2, λ = 2 and λ = 4. The eigenspaces are

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