###### Exercise9

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

1. What can you say about the pivot positions of $$A\text{?}$$

2. What can you say about the span of the columns of $$A\text{?}$$

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

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

in-context