# How do you solve using gaussian elimination or gauss-jordan elimination, #x-2y+z=1#, #2x-3y+z=5#, #-x-2y+3z=-13#?

##### 1 Answer

#### Explanation:

Begin by creating the augmented matrix, or a matrix with the

We now perform *row operations* on the 3 rows in order to reduce the left portion of the augmented matrix to the identity form:

We can do any of the following:

- Swap any two rows
- Multiply a single row by a non-zero constant value
- Add/Subtract a constant multiple of a row to another row

Using the notation

We can do nothing further [useful]. Notice the bottom line has all zero values. This indicates that this system of equations does not result in a unique

Any value of

It's commonly the case for problems like this with infinite solutions that we define everything in terms of a template variable