# GRE Subject Test: Math : Determinants

## Example Questions

### Example Question #1 : Determinants

Given the following matrix, find the determinant, if possible.

There is no determinant.

Explanation:

Write the formula to find the determinant given a 2 by 2 matrix.

Substituting in the given matrix we are able to find the determinant.

### Example Question #1 : Determinants

Evaluate the determinant of the following matrix.

Explanation:

Remember, to evaluate the determinant of a matrix use the following:

The first step would be to write the determinant of the matrix:

Now we can evaluate:

### Example Question #1 : Determinants

Evaluate the determinant of the following matrix.

Explanation:

To find the determinant of a 3 x 3 matrix, we must use the following:

The first thing we must do is write the determinant:

Now we can proceed to evaluate the determinant

Notice that the numbers 2, 4, and 3 are being multiplied by the determinants of the 2x2 matrices so we have:

### Example Question #2 : Determinants

Find the determinant of the matrix:

Explanation:

Step 1: We need to recall how to find the determinant of a  matrix. To find the determinant of a  matrix, we need to use the equation , where =Determinant, and  are from the matrix.

Step 2: Identify a,b,c, and d in the original matrix.
a=first number on top row, b=second number on top row (next to a), c=first number on the bottom row, and d is the second number on the bottom row (next to c).

In this matrix, a=, b=, c=, and d=.

Step 3: Substitute the values of a,b,c, and d into the equation to find the determinant of the matrix.

We will simplify the right side.

. We see that there are two negative signs in the middle, which will become a plus sign.

. Simplify the right side.

is the determinant.

The determinant of the matrix is .

### Example Question #2 : Determinants

Find the determinate of Matrix A.