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## Homework Statement

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] ℝ

^{7}.

1. What is the rank of M.

2. Do the columns of M, considered as vectors in ℝ

^{12}, span ℝ

^{12}.

## Homework Equations

## 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 ℝ

^{7}does that automatically mean the vectors can't span ℝ

^{12}and aside from that a set of all 0s can't span ℝ

^{7}can it?