The

**determinant**is a value calculated from an matrix. The determinant of a matrix, A, can be denoted as det(A), det A, or |A|. There are many uses for determinants. The determinant can be used to solve a system of equations. The determinant can tell you if the matrix is invertible or not (it is not if the matrix is 0).

We will discuss three ways to solve three different types of matrices.

**Determinant of a 2x2 matrix:**

**Determinant of a 3x3 matrix:**

**Determinant of a nxn matrix that is 4x4 or larger:**

1. Put the matrix in REF (

__here__is the blog post on REF for reference)

2. Calculate the product of the elements in the diagonal

- Make note of how many times you swapped rows to achieve putting the matrix in REF

- If no rows were swapped, this is the determinant

3. If rows were swapped, multiply the product of the elements in the diagonal by (-1) raised to the number of times rows were swapped. This will give you the determinant.

- Swapping rows changes the sign of the determinant

Let’s see some examples to better understand how to calculate the determinant.

First example (click

__here__):

__here__):

__here__):

Note that rows were swapped 3 times to achieve putting the matrix in REF.

2. Calculate the product of the diagonal

__Practice__. Next blog post, I will talk about a shortcut for calculating the inverse of a 2x2 matrix, using its determinant.

Until next time,

Leah

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