Constructing Matrix E and F for RowA and NulA Basis | Homework Explanation

[future_phd]

Homework Statement

Construct a matrix E such that its rows are the basis vectors for rowA and a matrix F such that its columns are the basis vectors for nulA. Compute EF. Explain your results.

Homework Equations

Basis for NulA was { [3 2 1 0], [1 3 0 1] } (except vertical)
Basis for RowA was { [1 0 2 4], [0 1 3 2] } (except vertical)

The Attempt at a Solution

I computed EF and I got the zero matrix, but I'm not sure exactly why this is the case. Can someone provide some insight on this? Thanks.

 

[NoMoreExams]

What is nullspace?

 

[future_phd]

What is nullspace?

Edit: DOH, nevermind, I get it now. The null space is the vectors that get mapped to the zero vector by the matrix. So if you take the matrix's row space and multiply by each of the basis vectors of the nullspace, you will get zero vectors in return (or since it was a matrix of the basis vectors to the null space, you will get the zero matrix in return).