Consider the following matrix: A = 3000 0 3 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 < Select an answer > Question 13 A is diagonalizable A is not diagonalizable diagonalizohlo motrix holow and R-1AP-D for

In Exercises 23-26, use the method of Example 4.5 to find all of the eigenvalues of the matrix A. Give bases for each of the corresponding eigenspaces. 25.

a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving that if A is an nn symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that B2=A.