Ok so my hint for this was:

For 1.) Reduce (A^T)^T = A to echelon form (for your problem it already

is in echelon form) then transpose the non-zero rows. Or, reduce A^T to

echelon form then choose the columns of A^T which contain leading row

entries (i.e. pivots). There is, in this case, a third way: eyeball

A^T.

For 2.) Let w be in null(A) and v be in col(A^T). Then Aw = 0 and

v = A^Tx for some x. Compute w dot v = w^Tv = ...

For #1, I found the transpose of A to be:

[[1,0,0,0],[3,0,0,0],[-4,1,0,0],[2,-3,1,0],[-1,7,4,0],[6,0,-3,0]]

(6x4 matrix)

When I rref the transpose of A I get:

[1,0,0,0], [0,1,0,0], [0,0,1,0], [0,0,0,0], [0,0,0,0], [0,0,0,0]

The first 3 columns of pivots, if I did that correctly...but whats the basis? The first 3 columns in the orig?

And for #2

What's the nul(A) and when I multiply them I should get 0. So I will have some m * 3 matrix times another matrix? Dot product them?