(Solved): Question 2 only 1. Consider the vectors v1,v2 and v3 in R3 given by v1=101 ...

1. Consider the vectors $v_1,v_2$ and $v_3$ in ${\mathbb{R}}^3$ given by $v_1=?\begin{array}{r}1\\ 0\\ ?1\end{array}?,v_2=?\begin{array}{l}2\\ 5\\ 1\end{array}?\text{ and }{v}_3=?\begin{array}{r}0\\ ?4\\ 3\end{array}?$ (a) If possible, write the vector $v_3$ as a linear combination of $v_1$ and $v_2$. (b) Determine whether the set $\left\{v_1,v_2,v_3\right\}$ spans ${\mathbb{R}}^3$. 2. Let $v_1,v_2$ and $v_3$ be as given in the previous problem. Find a linearly independent subset of $\left\{v_1,v_2,v_3\right\}$ which spans $\mathrm{span}\left\{v_1,v_2,v_3\right\}$.