Find spanning set for N(A^T)

[hank]

I have a problem where I'm supposed to find the nullspace of the transpose of a matrix A.

Our professor told us that this is similar to finding the null space of A, where we find the reduced row echelon form of the transpose of A.

Here's the matrix:

A =

2 1 1 1
0 2 4 6
0 0 1 0

My problem is, I plug this matrix into my calculator (TI-83) and punch in rref(A^T), but my calculator gives me an ERR: INVALID DIM.

How can I solve this problem?

 

[galactus]

The reason your calculator gives an error is because it is not a square matrix.

The trnaspose is \(\displaystyle \begin{bmatrix}2&0&0\\1&2&0\\1&4&1\\1&6&0\end{bmatrix}\)

The rref is \(\displaystyle \begin{bmatrix}1&0&0\\0&1&0\\0&0&1\\0&0&0\end{bmatrix}\)

There are 4 vectors and the vector space is 3. Therefore, the kernel has only the 0 vector and the nullspace is {0}

 

[hank]

Ok, so it's ok for me just to add a row of 0s?