Exercise 9

Suppose that $A$ is a $12\times12$ matrix and that, for some vector $\bvec$, the equation $A\xvec=\bvec$ has a unique solution.

1. What can you say about the pivot positions of $A$?

2. What can you say about the span of the columns of $A$?

3. If $\cvec$ is some other vector in $\real^{12}$, what can you conclude about the equation $A\xvec = \cvec$?

4. What can you say about the solution space to the equation $A\xvec =\zerovec$?