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Solution of 3 equations in 3 unknowns

Find the value of c which makes it possible to solve. $$\left\{\begin{array} {c} u + v + 2w = 2\\ 2u + 3v - w = 5\\ 3u + 4v + w = c \end{array}\right.$$

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Hint: the equation says that $(2,5,c)$ is a linear combination of $(1,2,3)$, $(1,3,4)$, and $(2,-1,1)$. Can you describe the set of such linear combinations (and its dimension)? – Marc van Leeuwen Oct 9 '12 at 11:36
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Please STOP Reposting this question. There have been 7+ copies in the last hour. – Ragib Zaman Oct 9 '12 at 11:37

marked as duplicate by Henry, Henning Makholm, Brian M. Scott, Ragib Zaman, Martin Sleziak Oct 9 '12 at 11:49

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Add equations 1 and 2 to get

$$3u +4v + w = 7.$$

Compare to equation 3, you get $c=7$.

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