For each of the given characteristic polynomials state which

For each of the given characteristic polynomials, state which of the following is time. Justify your answer. The matrix A is definitely diagonalizable. The matrix A is definitely not diagonalizable. More information is needed to determine if A is diagonalizable. p, (A) = (A-2)(A+5)(A-1). Pm(A) = (A - 2)^3. Pm(A) = (A^2+4)(A-1). ju(A) = (A^2-9)(A-1).

Solution

Then A is diagonalizable if and only if A has n linearly independent eigenvectors.

i) matrix has three different eigen values that would give three distinct eigen vectors

Definitely Diagonalizable

ii) all repeated eigen values

diagonalizable , need to find out further

iii) complex wigen values .

Not diagonalizable

iv) lamda = 3 , -3 , 1 are distinct

matrix is diagonalizable