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I have to show that $a_4$ is in the span of the other 3 vectors $a_1,a_2,a_3$

\begin{bmatrix} 2 &1 & 3\\ 3 & -1 & 4 \\ 1 & 2 & -1 \\ 4 & 4 & 3 \\ 0 & 3 & 5 \\ & \end{bmatrix} My Maple code: with (LinearAlgebra);

A := <<2, 1, 3>,<3, -1, 4>,<1, 2, -1>,<4, 4, 3>,<0, 3, 5>>; Then i use ReducedRowEchelon to get the linear combination which is M=:{{1,0,0},{0,1,0},{0,0,1},{0,0,0}, {0,0,0} }.

How do i prove that $a_4$ which is {-3,-6,5,2,7} is in the span of the other 3 vectors?

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    Oh, dear! Please use LaTeX here to write mathematics, otherwise things like your question are hard to read. Refer to the FAQ section for direction2012-12-17
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    To do this, in general, I recommend checking out [this previous answer](http://math.stackexchange.com/a/56206/17349).2012-12-17
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    So that meaning a*a1+b*a2+c*a3=a4 a(2,3,1,4,0)+b(1,-1,2,4,3)+c(3,4,-1,3,5)=a42012-12-17
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    We already have a problem here, which may be a typo (a serious one) or simply a mistake in the question: all your vector are 3-dimensional...except $\,a_4\,$, which is 5-dimensiona (in spite of having written it with curly parentheses intead of <>, as the other ones). This can't be as $\,a_4\,$ doesn't even live in the same universe as the other vectors.2012-12-17
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    Well I just copy pasted from Maple for that Vector. Gonna read up on Latex and try to do it in that format ASAP2012-12-17
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    Hmmm...so the vectors are that matrix's columns? I would have never guessed that.2012-12-17
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    Yeah sry for misleading :)2012-12-17

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