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I want to find the vector $X$ by the following lines:
$$(1,-3,5) \cdot X=49$$ $$(4,1,-1) \cdot X = 0$$ $$(2,0,-3)\cdot X=-9$$ I would like to get some advice how to find him.
Thanks!

Mhenni Benghorbal
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Ofir Attia
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    Write $ X = (x,y,z)$. Then you get 3 equations $x-3y+5z =49, 4x+y-z=0,2x-3z=-9$. These you can solve for example with Gauss algorithm. –  Jul 13 '13 at 11:36
  • @André if the third criteria were $|X|=\sqrt{6}$ ( X mean vector-size ) what I need to do? – Ofir Attia Jul 13 '13 at 12:37

2 Answers2

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Hint: Assume the vector $X=(x,y,z)$ and then solve the system of equations.

Mhenni Benghorbal
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$b=\begin{pmatrix}49\\0\\-9\end{pmatrix}$,

$A=\begin{pmatrix}1&-3&5\\4&1&-1\\2&0&-3\end{pmatrix}$,

$x=A^{-1}*b$

$So, x=\begin{pmatrix}3\\-7\\5\end{pmatrix}$.

kaka
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  • @awllower Thanks for writing in Latex. – kaka Jul 13 '13 at 21:58
  • Not a problem a all. In any case, I think it suffices to indicate the method of matrix inverses, instead of explicitly calculating the answer, since Op wanted some hints. Of course I am not OP. :P – awllower Jul 14 '13 at 14:51