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Let:

$$\vec v=\left [\matrix { -2 \cr 0\cr 2}\right],\quad \vec u=\left [\matrix { 0 \cr 3 \cr 0}\right ]$$

What is the value of $a$ such that:

$$\vec w=\left [\matrix { a \cr 2 \cr -3}\right ]$$

...is a linear combination of $\vec u$ and $\vec v$?

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