A P and D are n Times n matrices Check the true statements b

A, P and D are n Times n matrices. Check the true statements below: If A is diagonalizable, then A has n distinct eigenvalues. A is diagonalizable if A has n distinct eigenvectors. If AP = PD, with D diagonal, then the nonzero columns of P must be eigenvectors of A. If A is invertible, then A is diagonalizable.

Solution

The statements are:

A. is False because if A is diagonalizable then A need not have n distinct eigen values.

B. is true because of the theorem statement that\" An nth order matrix is diagonalizable iff it possesses n linearly independent eigen vectors.

C. is true because of the definition of P is the modal matrix.

D. is true because if A is invertible then it has n linearly independent eigen vectors.