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Linear Algebra

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Moderate

Solve to get Vector in Span

LINALG-NWZXOG

Let:

$$S=\left\{ \left [\matrix { 1 \cr 1 \cr 1}\right], \left [ \matrix { a\cr -3 \cr 6 }\right ] \right \}$$

Find $a$ such that:

$$\vec v=\left [\matrix { 13 \cr 11 \cr-7}\right ]$$

...is in the span of $S$.