In this blog post, we’ll talk about another advanced matrix topic that uses the same concepts, Gauss Jordan Elimination.

The Gauss Jordan Elimination is a method of putting a matrix in row reduced echelon form (RREF), using elementary row operations, in order to solve systems of equations, calculate rank, calculate the inverse of matrix, and calculate the determinant of a matrix (we will cover this in the next few blog posts).

RREF is when a matrix qualifies for the following four characteristics:

- Each non-zero row has 1, called a leading 1, as their first non-zero entry
- Each column with a leading 1 has zeros in every other entry
- As you move down the rows, the leading 1 moves to the right
- All zero rows are at the bottom

Another thing to note: Unlike matrices in REF, matrices in RREF are unique.

Here are examples of matrices in RREF:

Here are guidelines on how to put a matrix in RREF:

- Put the matrix in REF
- If there are nonzero entries in the column of the leading coefficient in the first row, make them 0 by using the elementary row operations
- If the leading coefficient in the first row is not a 1, make it a 1 by multiply the row by the reciprocal (this turns the leading coefficient into the leading 1)
- Repeat steps 2-3 and replace “first” with “second”, then “third”, and so on

Gauss Jordan Elimination can be tricky the first few times, so I will walk you through 3 examples.

First example (

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Example 3 (

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For more help or practice on this topic, visit Symbolab’s

__Practice__.

Until next time,

Leah.

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