Question: 17. Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such

17. Determine whether or not the given matrix A is diagonalizable. If

17. Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such that P'AP=D. [300] 030 Select the correct choice below and, if necessary. fil in the answer box to complete your choice. OA. The matrix is diagonalizable. (P.D) = L (Use a comma to separate matrices as needed.) OB. The matrix is not diagonalizable.

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To determine if the given matrix A is diagonalizable we need to find the eigenvalues and eigenvectors The matrix A is A beginbmatrix 3 0 0 0 3 0 0 0 2 endbmatrix Steps to Solve Step 1 Find the Eigenvalues For a diagonal matrix the eigenvalues are simply the entries on the main diagonal Thus the eigenvalues of this matrix are lambda1 3 lambda2 3 and lambda3 2 Step 2 Find the Eigenvectors 1 Eigenvalue lambda 3 Solve A 3Imathbfv 0 where I is the identity matrix A 3I beginbmatrix 0 0 0 0 0 0 0 0 1 endbmatrix For A 3Imathbfv 0 any vector of the form beginbmatrix x y 0 endbmatrix is a solution Eigenvectors beginbmatrix x y 0 endbmatrix where x y are free variables 2 Eigenvalue lambda 2 Solve A 2Imathbfv 0 A 2I beginbmatrix 1 0 0 0 1 0 0 0 0 endbmatrix For A 2Imathbfv 0 the vector beginbmatrix 0 0 z endbmatrix is a solution Eigenvector ... View full answer

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