Find the nullity and rank of a 3x5 matrix C where three columns = 0? Tricky problem. So I have a 3x5 matrix C, where {s,t,u,v,w} (I'm assuming those are its columns) is a linearly independent set of vectors in R^5, and that Cu=0, Cv=0, Cw=0.
What is the rank and nullity of C?
I'm guessing with the latter part of the question that Cu, Cv, and Cw are linearly independent in R^3, meaning the other two (Cs and Ct) are free columns, making the nullity equal to 2 and thus making the rank equal to 3. This is a wild guess, so it's probably wrong.

The homogeneous system $CX$=$0$ has at least 3 linearly independent solutions viz. $u,v,w$ (which you wrongly took as its columns) thereby giving Nullity(C)  is at least 3. Using Rank(C)+Nullity(C)=5, we get Rank(C) is at most 2.
