3. Consider the following matrix A: A: || 0 1 2 1 10 422 For each value of λ given below determine if it is an eigenvalue of A. a) λ = 0 b) λ = -1 c) λ = -2

Consider the following matrix: A = ..comm 3 0 0 00 03 0 -5 0-12 -3 12 000-2 a) Find the distinct eigenvalues of A, their multiplicities, and the corresponding number of basic eigenvectors. Number of Distinct Eigenvalues: 1 Eigenvalue: 0 has multiplicity 1 and corresponding number of basic eigenvectors 1 b) Determine whether the matrix A is diagonalizable. Conclusion: A is diagonalizable Question 13 A is diagonalizable A is not diagonalizable sk dom A in the diagonalizablo matrix boloy and P-1AP-D for

Consider the following matrix: A = 1 0-3 -9 -9 -2 2 -6 -18 -18 002 0 0 00 -3 -8 -9 003 10 11 a) Find the distinct eigenvalues of A, their multiplicities, and the dimensions of their associated eigenspaces. Number of Distinct Eigenvalues: 1 Eigenvalue: 0 has multiplicity 1 and eigenspace dimension 1 b) Determine whether the matrix A is diagonalizable. Conclusion: A is diagonalizable A is not diagonalizable SUBMIT AND MARK SAVE AN

Find bases for the eigenspaces associated with each eigenvalue of the matrix 3 0 0 -2 3-2 2 0 5 Find, if possible, a nonsingular matrix P such that P-¹AP is diagonal. A =

1 3 is diagonalizable. Its eigenvectors are: 4 2 The matrix A = 3. 2 4 3 4