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.