In mathematics we call a matrix as augmented matrix when we append two matrix columns. After appending the columns of two matrices the new matrix formed is known as augmented matrix. Here we will learn how to solve augmented matrix. If there are two matrices 'A' and 'B' then its augmented matrix will be represented as (A|B). Augmented matrix can be used in solving Linear Equations.
When we represent augmented matrix in form of equation then each row denotes constants from one equation and column represents the coefficient of variables.
Let us take an example to better understand the procedure of augmented matrix. We have three equations which will make a 3 * 3 matrix.
a – 2b + 3c = 7,
2a + b + c = 4,
-3a + 2b – 2c = -1,
From above equations first column represents coefficients of 'a', second column will represent all coefficients of 'b', and third column will represent coefficients of 'c'. Last column will represent constant values on other side.
First, second and third rows represent constant values of first, second and third equations respectively.
Here we have to make matrix 'A' as identity matrix. The order of matrix will be equal to number of equations. We have three methods to convert it into identity matrix.
We apply these three methods given below.
Method 1: Interchange values of one row from another row and replace the values of these rows.
Method 2: By multiplying values of a row with a constant value we can get the solution.
Method 3: Now subtract values of a row from values of another row.
Applying these three methods we get identity matrix. Values of matrix 'B' in matrix (A|B) will be equals to corresponding values for variables a, b and c.