# YALin.Alg.T: Subspaces

#### Ricemarine

##### Lifer
If matrix B = [3 1, 4 0, 0 2] (<-- row 1, row2, row 3), find matrix A such that Nul A = Col B.
So, right off the bat.
- A has two free variables (if A is in Rm, would A be in R2?)
- B has two pivots, which the vectors are (3,4,0) and (1,0,2)

The first may be partially wrong wrong, because NulA would have to reduce to ColB, which means that it would have to be in R3 instead of R2. Thus, A must be at least a 3X3 matrix.

As for the rest, I'm lost as to how to go about it... (giving me the answer wouldn't be of help, so probably logicial reasoning would be helpful).

Thanks for helping (I'm still trying to figure it out as we speak.).

#### RandomFool

##### Diamond Member
Math! so that's what this thread is about...

#### Ricemarine

##### Lifer
Originally posted by: RandomFool
Math! so that's what this thread is about...
Yeahh....

Anywho... still trying to think...
for a matrix to have two free variables in R3, two of the rows would have to cancel out with each other to remain a 3X3 matrix... Otherwise it would have to be a 4X3 matrix to have 2 free variables... Hmm...