Find all (real) values of k for which a is diagonalizable. (enter your answers as a comma-separated list.)a = [4 k0 4 ] k =

K needs to be equal to zero.

Step-by-step explanation:

The matrix is:

A matrix is diagonalizable if

A = P*D*P^(-1)

Where D is a diagonalized matrix formed with the eigenvalues of A, and P is a matrix formed with the eigenvectors of A.

We want to find the values of k that allow us to diagonalize this matrix.

A matrix is diagonalizable if:

The eigenvalues of A can be calculated by:

P(a) = det(A - x*I) = (4 - x)^2 =  the eigenvalues are 4 two times.

then eigenvectors are such:

A*v = 4*v

So the eigenvectors are:

then we will have that:

and, P^-1 = I^-1 = I

then:

A = I*D*I

every matrix multiplied by the identity is the same matrix:

A = I*D*I = D

then we have that A must be equal to D, then k must be zero,