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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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    Yeah sry for misleading :)2012-12-17

1 Answers 1

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I am making an example here for you in Maple, so you can do yours as well. I think it inspires you well. Assume you have 3 vector as: $u=\langle 2,1,-3,1 \rangle, v=\langle -1,3,5,0 \rangle,w=\langle 2,-1,1,-3 \rangle$ and want to find scalars in which we can write the vector $b=\langle -16,17,37,3 \rangle$ as their combinations. You can do by:

[>with(linalg):

[> u:=matrix(4,1,[2,1,-3,1]):

[> v:=matrix(4,1,[-1,3,5,0]):

[> w:=matrix(4,1,[2,-1,1,-3]):

[> b:=matrix(4,1,[-16,17,37,3]):

[> A:=augment(u,v,w):

[> linsolve(A,b);

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    @amWhy: Again, it is Maple :-)2013-04-13