Augmented matrix is a matrix having an extra column of constants separated by vertical line along with the given matrix elements.
Consider the two equations
ax + by = 0
cx + dy = 6

The augmented matrix is given as
Augmented Matrix
Augmented Matrix Calculator solves the given augmented matrix and finds the value of the variable.
Let us understand how to solve the augmented matrix using steps.
  1. Write the equation in terms of augmented matrix
  2. Interchange the two rows
  3. Multiply the rows by non zero constants
  4. Add one row with the another.

Below are given some problems based on solving Augmented matrix which may be helpful for you.

Solved Example

Question: Find the augmented matrix of the following equation:
4y = 20
6x + 2y = 6
Solution:
 
The given equations are
4y = 20
6x + 2y = 6
The Matrix is $\begin{bmatrix} 0 & 4 & |20\\ 6 & 2 & |6 \end{bmatrix}$
Step 1:
Interchange the given two rows
$\begin{bmatrix} 6 & 2 & |6\\ 0 & 4 & \ |20 \end{bmatrix}$

Step 2: Multiply the first row by 6 i.e., R1 --> $\frac{R_{1}}{6}$
$\begin{bmatrix} 1 & \frac{1}{3} & |1\\ 0 & 4 & \ |20 \end{bmatrix}$
Then multiply the second row by 4 ie., R2 --> $\frac{R_{2}}{4}$
$\begin{bmatrix} 1 & \frac{1}{3} & |1\\ 0 & 1 & \ |5 \end{bmatrix}$

Step 3 : Add the first row with the another R1 --> R1 - $\frac{1}{3}$ R2
$\begin{bmatrix} 1 & 0 & | - \frac{2}{3} \\ 0 & 1 & \ |5 \end{bmatrix}$

The values of equation using augmented matrix are
x = - $\frac{2}{3}$ = - 0.667
y = 5.