Let M be the 12 x 7 coefficient matrix of a homogeneous linear system, and suppose that this system has the unique solution 0 = (0, ..., 0) [itex]\in[/itex] ℝ7.
1. What is the rank of M.
2. Do the columns of M, considered as vectors in ℝ12, span ℝ12.
The Attempt at a Solution
1. Well since the matrix is a homogeneous matrix the rank of M can be from 0 [itex]\leq[/itex] rankM [itex]\leq[/itex] 7.
so then rank has a rank of 7 I believe
2. I'm not sure how to solve this but if the solution is in ℝ7 does that automatically mean the vectors can't span ℝ12 and aside from that a set of all 0s can't span ℝ7 can it?