Suppose $L: M(4,3) \to R^7$ is linear and onto.
- Determine the rank L.
- Determine the nullity L.
I know that rank is equal to the leading 1's in a reduced row echelon matrix, and the nullity is equal to the number of columns corresponding to free variables. So if I was given an actual matrix I could easily find the rank and nullity, however, I'm not given an exact matrix, only M(4,3). Does that mean I should assume the matrix looks like this:
1 0 0 0 1 0 0 0 1 0 0 0
Therefore the rank is 3 and the nullity is 0? Thus the dimension of M is 3 since:
rank L + nullity L = dim M ?