Exercise 1.1.23

Question

If you look at all combinations of those $u, v$, and $w$, is there any vector that can't be produced from $c \boldsymbol{u}+d \boldsymbol{v}+e \boldsymbol{w}$ ? Different answer if $\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}$ are all in ____.

Prakash Anand · Accepted Answer

All vectors are combinations of $\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}$ as drawn (not in the same plane). Start by seeing that $c \boldsymbol{u}+d \boldsymbol{v}$ fills a plane, then adding $e \boldsymbol{w}$ fills all of $\mathbf{R}^{3}$.

Exercise 1.1.23

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Exercise 1.1.23

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