1 consider the matrix A= 0 2 0 30 whose characteristic polynomial is given by 0...

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1 consider the matrix A= 0 2 0 30 whose characteristic polynomial is given by 0 1 det(A - λI) = −(λ + 1)(λ − 3)² Find an invertible matrix P that diagonalizes A, that is, such that D = P-¹AP is a diagonal matrix of eigenvalues. Explain clearly whether the vector v = (1, 1, 1) is an eigenvector of matrix A. 1 consider the matrix A= 0 2 0 30 whose characteristic polynomial is given by 0 1 det(A - λI) = −(λ + 1)(λ − 3)² Find an invertible matrix P that diagonalizes A, that is, such that D = P-¹AP is a diagonal matrix of eigenvalues. Explain clearly whether the vector v = (1, 1, 1) is an eigenvector of matrix A.