##### Exercise1

Consider the set of vectors

\begin{equation*} \vvec_1 = \threevec{1}{2}{1}, \vvec_2 = \threevec{0}{1}{3}, \vvec_3 = \threevec{2}{3}{-1}, \vvec_4 = \threevec{-2}{4}{-1} \text{.} \end{equation*}
1. Explain why this set of vectors is linearly dependent.

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

3. Find weights $$c_1\text{,}$$ $$c_2\text{,}$$ $$c_3\text{,}$$ and $$c_4\text{,}$$ not all of which are zero, such that

\begin{equation*} c_1\vvec_1 + c_2 \vvec_2 + c_3 \vvec_3 + c_4 \vvec_4 = \zerovec \text{.} \end{equation*}
4. Find a nontrivial solution to the homogenous equation $$A\xvec = \zerovec$$ where $$A=\left[\begin{array}{rrrr} \vvec_1\amp\vvec_2\amp\vvec_3\amp\vvec_4 \end{array}\right]\text{.}$$

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