Question: Show that the matrix has eigenvalues 5, 3, 3. Find the corresponding eigenvectors. For the repeated eigenvalue, show that it has two linearly independent eigenvectors

Show that the matrix

-2 2-3] A = 2 1 -6 -1 -2 0

has eigenvalues 5, –3, –3. Find the corresponding eigenvectors. For the repeated eigenvalue, show that it has two linearly independent eigenvectors and that any vector of the general form

0 -2 3 1 + B 0 0

is also an eigenvector.

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