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## 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

Could someone please verify?

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?