###### Exercise4

Determine if the following statements are true or false and provide a justification for your response.

1. If $$\vvec_1,\vvec_2,\ldots,\vvec_n$$ are linearly dependent, then one vector is a scalar multiple of one of the others.

2. If $$\vvec_1, \vvec_2, \ldots, \vvec_{10}$$ are vectors in $$\real^5\text{,}$$ then the set of vectors is linearly dependent.

3. If $$\vvec_1, \vvec_2, \ldots, \vvec_{5}$$ are vectors in $$\real^{10}\text{,}$$ then the set of vectors is linearly independent.

4. Suppose we have a set of vectors $$\vvec_1,\vvec_2,\ldots,\vvec_n$$ and that $$\vvec_2$$ is a scalar multiple of $$\vvec_1\text{.}$$ Then the set is linearly dependent.

5. Suppose that $$\vvec_1,\vvec_2,\ldots,\vvec_n$$ are linearly independent and form the columns of a matrix $$A\text{.}$$ If $$A\xvec = \bvec$$ is consistent, then there is exactly one solution.

in-context