Determinant Calculator

Tutorial

The determinant is a number that we can calculate from any square matrix.

Why do we use determinants?

We use determinants to:

1. Find out if the matrix has an inverse.

2. Find an inverse of a square matrix.

3. Solve the system of linear equations.

4. Find the characteristic polynomial, eigenvalues and eigenvectors.

Determinant 2 x 2

For any matrix with 2 rows and 2 columns, the determinant can be calculated using the formula:

Example

Find the determinant of

Using the above formula, we have:

|A| = 4·3-(-3)·2 =
= 12 + 6 = 18

Determinant 3 x 3

The determinant of a 3x3 matrix can be solved using the determinants of the 2x2 matrices using the formula:

Example

Find the determinant of

Using the determinant formula for 3x3 matrices, we have