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Are the following set of vectors in R^4 linearly independent?
\[\left\{ (1,0,2,1),(1,2,1,0),(1,1,0,1) \right\}\]
I want to get the set of vectors into matrixform but the "set" term confuses me a bit. Is this the right form?
\[\left[\begin{matrix}1 & 0 &2&1 \\1 & 2 &1&0 \\1 & 1&0&1\end{matrix}\right]=\left[\begin{matrix}0 \\ 0 \\0\end{matrix}\right]\]
Or is it the other way around?
 one year ago
 one year ago
Are the following set of vectors in R^4 linearly independent? \[\left\{ (1,0,2,1),(1,2,1,0),(1,1,0,1) \right\}\] I want to get the set of vectors into matrixform but the "set" term confuses me a bit. Is this the right form? \[\left[\begin{matrix}1 & 0 &2&1 \\1 & 2 &1&0 \\1 & 1&0&1\end{matrix}\right]=\left[\begin{matrix}0 \\ 0 \\0\end{matrix}\right]\] Or is it the other way around?
 one year ago
 one year ago

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Outkast3r09Best ResponseYou've already chosen the best response.0
you need to add a row o zeroes
 one year ago

frxBest ResponseYou've already chosen the best response.0
Add a row of zeroes, what do you mean by that?
 one year ago

frxBest ResponseYou've already chosen the best response.0
That's how i ussualy write it, is that what you meant?
 one year ago

amoodaryaBest ResponseYou've already chosen the best response.1
a(1,0,2,−1)+b(1,2,−1,0)+c(1,1,0,−1)=(0,0,0,0) they are independent if only a=b=c=0 multiply them and solve the system of equation
 one year ago

amoodaryaBest ResponseYou've already chosen the best response.1
a+b+c=0 0a+2b+c=0 2ab+0c=0 1a+0bc=0
 one year ago

frxBest ResponseYou've already chosen the best response.0
\[a _{1}\left(\begin{matrix}1 \\0 \\ 2\\1 \end{matrix}\right)+a _{2}\left(\begin{matrix}1 \\2 \\ 1\\0\end{matrix}\right)+a _{3}\left(\begin{matrix}1 \\1 \\ 0\\1\end{matrix}\right)=\left(\begin{matrix}0 \\0 \\ 0\\0\end{matrix}\right)\] \[\left[\begin{matrix}1 & 1 & 1 \\0 & 2 & 1 \\ 2 & 1 & 0 \\1 & 0 & 1 \end{matrix}\right]=\left(\begin{matrix}0 \\ 0 \\ 0 \\0\end{matrix}\right)\] \[\left[\begin{matrix}1 & 0 &0 \\0& 1 & 0 \\ 0&0&1 \\ 0&0&0\end{matrix}\right]=\left[\begin{matrix}0 \\ 0 \\0\\0\end{matrix}\right]\]
 one year ago

frxBest ResponseYou've already chosen the best response.0
@amoodarya How should i interpret the reduced matrix, 000=0 but also 001=0 ?
 one year ago

frxBest ResponseYou've already chosen the best response.0
So it can't really be a_3=t it must be a_3=0 and a_1=a_2=a_3=0 and the vectors are linearly independent, am I correct?
 one year ago

amoodaryaBest ResponseYou've already chosen the best response.1
do you "rank of matrix" ?
 one year ago

frxBest ResponseYou've already chosen the best response.0
Don't really know what rank of matrix is, will have to look it up.
 one year ago

frxBest ResponseYou've already chosen the best response.0
@amoodarya So the number of linearly independent vectors in the basis is three, so the rank should be three too, but what does this say about the dependent/independent case?
 one year ago
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