##### Exercise5

Suppose we have a set of vectors $$\vvec_1,\vvec_2,\vvec_3,\vvec_4$$ in $$\real^5$$ that satisfy the relationship:

\begin{equation*} 2\vvec_1 - \vvec_2 + 3\vvec_3 + \vvec_4 = \zerovec \end{equation*}

and suppose that $$A$$ is the matrix $$A=\left[\begin{array}{rrrr} \vvec_1\amp\vvec_2\amp\vvec_3\amp\vvec_4 \end{array}\right] \text{.}$$

1. Find a nontrivial solution to the equation $$A\xvec = \zerovec\text{.}$$

2. Explain why the matrix $$A$$ has a column without a pivot position.

3. Write one of the vectors as a linear combination of the others.

4. Explain why the set of vectors is linearly dependent.

in-context