# Rank of 5x3 matrix A is 3, what is RREF(A)?

• pyroknife

## Homework Statement

Matrix A is of size 5x3 (5 rows and 3 columns) with rank(A)=3. Find the reduced row echlon form of A

## The Attempt at a Solution

Rank(A)=3 thus, there are 3 pivot variables. Since there are 3 pivot variables and 3 columns=> no free variables, thus we have 2 rows of zeroes at the bottom. The top 3 rows represent a 3x3 identity matrix.
[/B]
It seems like the answer is just
1 0 0
0 1 0
0 0 1
0 0 0
0 0 0

I was curious if the question was instead a 3x5 matrix.
For this scenario I observe the following:
1) There will be 3 pivots, but since there are 5 columns, there will be 2 free variables.
2) I think RREF(A) can be 4!=4*3*2=24 different matrices?

pyroknife said:

## Homework Statement

Matrix A is of size 5x3 (5 rows and 3 columns) with rank(A)=3. Find the reduced row echlon form of A

## The Attempt at a Solution

Rank(A)=3 thus, there are 3 pivot variables. Since there are 3 pivot variables and 3 columns=> no free variables, thus we have 2 rows of zeroes at the bottom. The top 3 rows represent a 3x3 identity matrix.
[/B]
It seems like the answer is just
1 0 0
0 1 0
0 0 1
0 0 0
0 0 0