Exercise 1.1.6

Question

Every combination of $\boldsymbol{v}=(1,-2,1)$ and $\boldsymbol{w}=(0,1,-1)$ has components that add to _______. Find $c$ and $d$ so that $c \boldsymbol{v}+d \boldsymbol{w}=(3,3,-6)$. Why is $(3,3,6)$ impossible?

Prakash Anand · Accepted Answer

The components of every $c \boldsymbol{v}+d \boldsymbol{w}$ add to zero because the components of $\boldsymbol{v}$ and of $\boldsymbol{w}$ add to zero. $c=3$ and $d=9$ give $(3,3,-6)$. There is no solution to $c \boldsymbol{v}+d \boldsymbol{w}=(3,3,6)$ because $3+3+6$ is not zero.

Exercise 1.1.6

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Exercise 1.1.6

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