Exercise 1.1.18

Question

Restricted by $0 \leq c \leq 1$ and $0 \leq d \leq 1$, shade in all combinations $c v+d w$.

Prakash Anand · Accepted Answer

The combinations $c \boldsymbol{v}+d \boldsymbol{w}$ with $0 \leq c \leq 1$ and $0 \leq d \leq 1$ fill the parallelogram with sides $\boldsymbol{v}$ and $\boldsymbol{w}$. For example, if $\boldsymbol{v}=(1,0)$ and $\boldsymbol{w}=(0,1)$ then $c \boldsymbol{v}+d \boldsymbol{w}$ fills the unit square. But when $\boldsymbol{v}=(a, 0)$ and $\boldsymbol{w}=(b, 0)$ these combinations only fill a segment of a line.

Exercise 1.1.18

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Exercise 1.1.18

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