# Matrices

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More Lessons for Intermediate Algebra or Algebra II

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
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In this lesson, we will learn

• how to add, subtract and perform scalar multiplication with matrices
• how to multiply two matrices
• how to use augmented matrices

### Introduction to Matrices

A matrix is a way that we organize large amounts of data. An introduction to matrices and matrix operations is very important, especially when we get into upper-level mathematics. Matrices come in various dimensions and we write the dimensions of a matrix as the number of rows x the number of columns. We can also identify a specific figure in the matrix by writing the row location and the column location.

Introduction to Matrices

### Matrix Operations

When working with matrices, we can perform a number of matrix operations including matrix addition and subtraction. When adding or subtracting matrices, we first need to ensure that the matrices have the same dimensions, which is the number of rows times the number of columns. If they have the same dimensions, then we simply add or subtract the numbers in the corresponding locations.

Matrix Operations - Adding, Subtracting, and Multiplying by a constant for matrices is discussed.
This video shows how to add, subtract and perform scalar multiplication with matrices.

### Matrix Multiplication

When working with matrices, we can perform a number of matrix operations including matrix multiplication. When multiplying matrices, we first need to ensure that the matrices have the same dimensions, which is the number of rows times the number of columns. The resulting matrix after multiplication has the dimensions of the outer two dimensions. Each value is equal to the product of the corresponding row and column.

This video explains how to multiply matrices.

This video shows how to multiply matrices.
This video demonstrates how to perform matrix multiplication.

### Augmented Matrices

To solve a system of linear equations, we can use substitution, elimination or something we call augmented matrices. To use matrices to solve a system of linear equations, we first enter the values associated with each of the variables and the answer. Once we put the information into a matrix, we can use matrix operations to solve.

This video introduces augmented matrices for the purpose of solving systems of equations. It also introduces row echelon and reduced row echelon form.

This video shows how to transform and augmented matrix to row echelon form to solve a system of equations.
This video shows how to transform and augmented matrix to reduced row echelon form to solve a system of equations.

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