the matrix has eigenvalues 0, 2, and 4.
(2 0 2
0 2 0
2 0 2)
determine corresponding eigenvectors.

The eigenvectors of the matrix are , and .

Step-by-step explanation:

The given matrix is

It is given that the matrix has eigenvalues 0, 2, and 4.

For

Using Row operations we get

Let z=1,

At eigen vector is .

Similarly,

For

Using row operations.

At eigen vector is .

For

Using row operations.

at z=1

At eigen vector is .

Therefore the eigenvectors of the matrix are , and .

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