##### Exercise6

Suppose that $$\vvec_1,\vvec_2,\ldots,\vvec_n$$ is a set of vectors in $$\real^{27}$$ that form the columns of a matrix $$A\text{.}$$

1. Suppose that the vectors span $$\real^{27}\text{.}$$ What can you say about the number of vectors $$n$$ in this set?

2. Suppose instead that the vectors are linearly independent. What can you say about the number of vectors $$n$$ in this set?

3. Suppose that the vectors are both linearly independent and span $$\real^{27}\text{.}$$ What can you say about the number of vectors in the set?

4. Assume that the vectors are both linearly independent and span $$\real^{27}\text{.}$$ Given a vector $$\bvec$$ in $$\real^{27}\text{,}$$ what can you say about the solution space to the equation $$A\xvec = \bvec\text{?}$$

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