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Decided to solve the problems from last year's exams. I came across this example. Honestly, I didn't understand it. Who can help a young student?

Find characteristic equation of the matrix A in the form of the polynomial of degree of 3 (you do not need to find eigenvalues) and associated eigenvectors of the matrix. Eigenvalues of the matrix: -2, -2, 1.

А= 7 0 -3

-9 -2 3

18 0 -8