Final answer:
An augmented matrix is a way to represent a system of linear equations using a matrix. To find the solutions, we can perform row operations on the augmented matrix to reduce it to row echelon form or reduced row echelon form.
Step-by-step explanation:
An augmented matrix is a way to represent a system of linear equations using a matrix. The augmented matrix is obtained by adding a column on the right side of the coefficient matrix, which contains the constants from the equations. For example, if we have the system of equations:
2x + 3y = 7
4x - 2y = 6
The augmented matrix would be:
[2 3 | 7]
[4 -2 | 6]
To find the solutions, we can perform row operations on the augmented matrix to reduce it to row echelon form or reduced row echelon form. Each row operation represents an equivalent system of equations. The solutions can be found by interpreting the rows in the augmented matrix.