Given matrix A = [1 -1 -1 0 1 -2 0 1 4] and matrix B = [1 0 0 0 2 -0 0 0 3]. Usi

Question

Given matrix A = [1 -1 -1 0 1 -2 0 1 4] and matrix B = [1 0 0 0 2 -0 0 0 3]. Using the fact that matrix A is similar to matrix B, determine the eigenvalues for matrix A. Given lambda_1 = 2, lambda_2 = -2, lambda_3 = 3 are the eigenvalues for matrix A where A = [1 1 -3 -1 3 1 -1 1 -1] In addition, given the eigenvectors corresponding to the above eigenvalues respectively X_1 = (-1, 0, 1), XX = (1, -1, 4), X_3 = (-1, 1, 1), determine the matrix P such that P^-1 AP = D where Determine matrix A is diagonalizable given matrix A = [1 0 0 - 2 0 0 1 1 -3]. Justify your answer. Matrix A is diagonalizable since ___ Matrix A is not diagonalizable since ____

Explanation / Answer

1) Since the similar matrices have same eigen values so the eigen values of A are same as eigen values of B

Now B is a diagonal matrix so its eigen values are the diagonal entries

That is Eigen values of B are 1 , 2 , and 3.

Hence Eigen values of A are 1 , 2 , and 3.

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