Exercise 10

Suppose that $$\vvec_1 = \fourvec{3}{1}{3}{-1}, \vvec_2 = \fourvec{0}{-1}{-2}{2}, \vvec_3 = \fourvec{-3}{-3}{-7}{5}$$.

1. Is $\vvec_3$ a linear combination of $\vvec_1$ and $\vvec_2$? If so, find weights such that $\vvec_3 = a\vvec_1+b\vvec_2$.

2. Show that a linear combination $$a\vvec_1 + b\vvec_2 + c\vvec_3$$ can be rewritten as a linear combination of $\vvec_1$ and $\vvec_2$.

3. Explain why $\laspan{\vvec_1,\vvec_2,\vvec_3} = \laspan{\vvec_1,\vvec_2}$.