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Matrices

Solving system of equations using the augmented matrix
A system of equations is when we have more than one equation and more than one variable. For example:

They can be solved using the augmented matrix:

We must use elementary row operations to change the coefficient matrix to an identity matrix.

Solve this system of equations using an augmented matrix:
Augmented matrix :

Then:

5y=-55, so y=-11
3x-2·(-11)=13
3x+22=13
3x=13-22
3x=-9
x=-3
Solution: (-3,-11)

Solve using the augmented matrix

 $\left.\begin{matrix}2x-y-4z=4\\-x-4y-5z=3\\-4x+5z=-2\\nd{matrix}\right\}$ X =