###### Exercise3

1. If the vectors $$\vvec_1$$ and $$\vvec_2$$ form a linearly dependent set, must one vector be a scalar multiple of the other?
2. Suppose that $$\vvec_1,\vvec_2,\ldots,\vvec_n$$ is a linearly independent set of vectors. What can you say about the linear independence or dependence of a subset of these vectors?
3. Suppose $$\vvec_1,\vvec_2,\ldots,\vvec_n$$ is a linearly independent set of vectors that form the columns of a matrix $$A\text{.}$$ If the equation $$A\xvec = \bvec$$ is inconsistent, what can you say about the linear independence or dependence of the set of vectors $$\vvec_1,\vvec_2,\ldots,\vvec_n,\bvec\text{?}$$