# GRE Subject Test: Math : Eigenvalues

## Example Questions

### Example Question #1 : Eigenspace Classifications

Find the eigenvalues of the following matrix, if possible.

Possible Answers:

The eigenvalues do not exist.

Correct answer:

Explanation:

In order to find the eigenvalues of a matrix, apply the following formula:

is the identity matrix.

Compute the determinant and set it equal to zero.

Solve for lambda by using the quadratic formula.

### Example Question #2 : Eigenspace Classifications

Find the eigenvalues of the following matrix, if possible.

Possible Answers:

The eigenvalues do not exist.

Correct answer:

Explanation:

In order to find the eigenvalues of a matrix, apply the following formula:

is the identity matrix.

Compute the determinant and set it equal to zero.

Solve for lambda by using the quadratic formula.