##### Exercise3

Consider the vectors

\begin{equation*} \vvec_1 = \left[\begin{array}{r} 2 \\ 1 \end{array} \right], \vvec_2 = \left[\begin{array}{r} -1 \\ 1 \end{array} \right], \vvec_3 = \left[\begin{array}{r} -2 \\ 0 \end{array} \right] \end{equation*}
1. Find the linear combination with weights $$c_1 = 2\text{,}$$ $$c_2=-3\text{,}$$ and $$c_3=1\text{.}$$

2. Can you write the vector $${\mathbf 0} = \left[\begin{array}{r} 0 \\ 0 \end{array}\right]$$ as a linear combination of $$\vvec_1\text{,}$$ $$\vvec_2\text{,}$$ and $$\vvec_3\text{?}$$ If so, describe all the ways in which you can do so.

3. Can you write the vector $${\mathbf 0} = \left[\begin{array}{r} 0 \\ 0 \end{array}\right]$$ as a linear combination using just the first two vectors $$\vvec_1$$ $$\vvec_2\text{?}$$ If so, describe all the ways in which you can do so.

4. Can you write $$\vvec_3$$ as a linear combination of $$\vvec_1$$ and $$\vvec_2\text{?}$$ If so, in how many ways?

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