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I have the following system:

$$\left\{\begin{array}{cccccccc} 2x&+&3y&+&z&-&3v&=&2 \\ x&-&y&+&2z&+&v&=&0\\ 3x&+&2y&+&3z&-&2v&=&-2 \end{array}\right.$$

I have to show if the system does or doesn't have solutions using multidimensional vectors. I notice that it has more unknowns than equations so it is an undetermined system. If I form the matrix , I notice that the determinant is different from zero so this three vectors are linearly indipendent.Now what do I do to show if they have a solution or not?

Note: I have to use only determinants and linearly independent/dependent vector theory to show it.

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    Since the appropriate matrix is $3\times 4$, the determinant is undefined. What do you mean by "determinant is different from zero"?2012-12-15
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    No, I form the matrix with the vectors ( 2 1 3) (3 -1 2) and (1 2 3) ,and here the determinant is diff from zero...I know I have to form another matrix including 2 0 -2 and find the determinant ,but I don't know how to form it..2012-12-15
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    @Beyonce45: So, what about the $v$'s??2012-12-15
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    @Beyonce45: I edited your question just because I think it is easier to read this way. Feel free to revert my changes if you think otherwise.2012-12-15

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