# 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 #191 : Algebra

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 #191 : Algebra

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.       Explanation:

Matrix A is given below. The formula for the determinate of a 2x2 matrix is: Plugging in the values gives us: ### All GRE Subject Test: Math Resources 