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
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:
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?