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 .

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

the answer is c. 23/3