Solve out the following system of equations by using augmented matrices.

3x - 3 y - 6 z = -3

2x - 2 y - 4 z = 10

-2x + 3 y + z = 7

Solution

Following is the augmented matrix for this system.

We can obtain a 1 into the upper left corner by dividing by the first row by a 3.

Next we'll obtain the two numbers under this one to be zeroes.

And we can end. The middle row is all zeroes apart from the final entry that isn't zero. Note that it doesn't matter what the number is as long as it isn't zero.

Once we reach this kind of row we know that the system won't contain any solutions and therefore there isn't any cause to go any farther.

Okay, let's see how we solve out a system of three equations along with an infinity number of solutions along with the augmented matrix method.  This instance will also illustrate an interesting idea regarding systems.