無年度 - 主題課程_對角化：特徵多項式和行列式#107845

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Please find the eigenvalues and eigenvectors of given

Let and f(s) = s⁴ - 13s³ + 17s² - 13s + 87. Please find f(A).

Let .Please find f(A), where f(t)=t⁴-3t³-6t²+7t+2.

If A is an nxn matrix, derive the characteristic polynomial of A.

(a) Find the eigenvalues of A

(b) Find the determinant of A

(c) Based on (a), state whether A is invertible or not

(a) What are the eigenvalues of this matrix?

(b) What are the eigenvectors of this matrix?

(c) What is the determinant of this matrix?

(d) When will this matrix have its inverse? Please tell us your reason.

(e) Please evaluate (A - 2I)(A - 4I)(A - 51) + A, where I is a 3-by-3 identity matrix.