What are Augmented Matrices?

To solve linear equations we have developed a method in which we combine two matrices made using those equations and thus, make it easier to solve those linear equations. This combined matrix is called an Augmented Matrices. The coefficient of the linear equations and the constant value associated with those equations are combined together to form a single matrix and this matrix is called an Augmented matrix. In Augmented Matrices, these two matrices are combined using their column values. Thus, if we have m columns in the first matrix and n columns in the second matrix, then in the augmented matrix we have (m + n) columns.

An augmented matrix is a means to solve simple linear equations. The coefficients and constant values of the linear equations are represented as a matrix, referred to as an augmented matrix. In simple terms, the augmented matrix is the combination of two simple matrices along the columns. If there are m columns in the first matrix and n columns in the second matrix, then there would be m + n columns in the augmented matrix.

The image added below a 3×3 matrix A and a 3×1 matrix B. Then the augmented matrix is [A|B] as shown in the image,

Augmented Matrix

Augmented Matrix is a matrix that is formed when we combine the columns of two matrices and thus, form a new matrix. The new matrix so formed is called the Augmented Matrix. An Augmented Matrix is important to solve various types of problems in mathematics especially those which involve the use of equations. Augmented Matrix is used to solve simple linear equations. An Augmented Matrix has the same number of rows as there are variables in the given linear equations.

This article deals with the concept of an Augmented Matrix, its properties, examples, and others in detail. it will also help us to understand how the augmented matrix is used to solve linear equations.

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What are Augmented Matrices?

To solve linear equations we have developed a method in which we combine two matrices made using those equations and thus, make it easier to solve those linear equations. This combined matrix is called an Augmented Matrices. The coefficient of the linear equations and the constant value associated with those equations are combined together to form a single matrix and this matrix is called an Augmented matrix. In Augmented Matrices, these two matrices are combined using their column values. Thus, if we have m columns in the first matrix and n columns in the second matrix, then in the augmented matrix we have (m + n) columns....

Augmented Matrix of a System of Linear Equation

Augmented Matrix is the combination of two matrices of the system of linear equations which contains the coefficient matrix and the constant matrix (column matrix) separated by a dotted line....

How to Find Augmented Matrix?

Agumented matrix is found by following the steps discussed below:...

How to Solve Augmented Matrix?

The solution to the system of the linear equation is easily found by simplifying the augmented matrix and transforming the same into an identity matrix by following the Gauss-Jordan Method of matrix transformation, or by simply using Row Operation or Column Operation on the augmented matrix. Using the row transformation we change the first part of the augmented matrix into the identity matrix and then values in the last column are the solution to the given linear equations....

Properties Of Augmented Matrix

Augmented matrix has various properties and some of the important properties of the augmented matrix are mentioned below:...

Inverse of Matrix Using Augmented Matrix

We can also find the inverse of any matrix by using the augmented matrix concept. Suppose we have 3 × 3 matrix A such that,...

Solved Examples on Augmented Matrix

Example 1: Find the augmented matrix of the system of equations,...

Practice Questions on Augmented Matrix

Q1: Find the Augmented Matrix for 2x + 3y = 2 and 3x – y = 1...

FAQs on Augmented Matrix

1. What is Augmented Matrix?...