Exercise 1.1.19

Question

Restricted only by $c \geq 0$ and $d \geq 0$ draw the "cone" of all combinations $c v+d w$.

Prakash Anand · Accepted Answer

With $c \geq 0$ and $d \geq 0$ we get the infinite "cone" or "wedge" between $\boldsymbol{v}$ and $\boldsymbol{w}$. For example, if $\boldsymbol{v}=(1,0)$ and $\boldsymbol{w}=(0,1)$, then the cone is the whole quadrant $x \geq 0, y \geq$ $0 .$ Question: What if $\boldsymbol{w}=-\boldsymbol{v}$ ? The cone opens to a half-space. But the combinations of $\boldsymbol{v}=(1,0)$ and $\boldsymbol{w}=(-1,0)$ only fill a line.

Exercise 1.1.19

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Exercise 1.1.19

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