# All About Matrices

### Adding, Subtracting, Multiplying, and Finding Determinants

## What is a Matrix?

By definition, a matrix is any rectangular array of variables or constants in horizontal rows and vertical columns. Matrices can also be used matrix equations, matrix forms used to represent a system of equations. The determinant of a matrix is a number that is calculated from a square matrix. A square matrix is when the matrix has the same number of columns as it does rows, such as a 2x2 matrix, or a 3x3 matrix. The determinant is useful for things such as systems of linear equations, or finding the inverse of a matrix.

## Adding and Subtracting Matrices

## Adding and Subtracting Matrices

When adding and subtracting matrices, the numbers of rows and columns must first be the same. For example, a 2x3 (2 rows by 3 columns) matrix can only be added to a matrix that is also 2x3. To perform the operation, you simply add or subtract the numbers that are in corresponding spots of each matrix. Examples are shown below:

Addition With Matrices - Demonstration/Tutorial

Subtraction With Matrices - Demonstration/Tutorial

## Multiplying Matrices

## Multiplying Matrices

When multiplying matrices, first, you must make sure that the number of columns of matrix A, and the number of rows of matrix B are equal. Then you multiply each row by each column and put the products into a new matrix. The resulting matrix should have the number of rows of matrix A, and the number of columns of matrix B. For example, if you multiplied a 3x4 by a 4x2, the matrix will be 3x2. An example is shown below:

Multiplication With Matrices || Demonstration

## Determinants

## Finding the Determinant of a Square Matrix

Determinants can always be found in square matrices. They do not result from non-square matrices. They can be found by in each of the scenarios below by the following steps:

Finding the Determinant of a 2x2 Matrix || Demonstration

## In a 3x3 matrix -

- Take the first two columns of the matrix and copy them to the right of the matrix
- Multiply the three numbers that are diagonal to each other in each of the columns
- Add those three numbers together
- Multiply the three diagonals going in the opposite direction
- Subtract those three numbers from the sum of the other numbers

Video example below:

Finding the Determinant of a 3x3 Matrix || Demonstration

## What Was Learned?

- What a matrix is
- How to add matrices together
- How to subtract matrices
- How to multiply matrices
- How to find the determinant of a matrix

Below is a quick tutorial on how to use matrices on a calculator -

Matrices on a Calculator Basics || Demonstration

## Upcoming Assessments -

Quiz #4 - Monday, December 7th

Test #2 - Thursday, December 10th