(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

if x[tex]_{1}[/tex]=[tex]

\begin{pmatrix}2 \\ 1 \\ 3\end{pmatrix}

[/tex]

x[tex]_{2}[/tex]=[tex]

\begin{pmatrix}3 \\ -1 \\ 4\end{pmatrix}

[/tex]

x[tex]_{3}[/tex]=[tex]

\begin{pmatrix}2 \\ 6 \\ 4\end{pmatrix}

[/tex]

(i) show that x1,x2 and x3 are linearly dependent

(ii) show that x1 and x2 are linearly independent

(iii)what is the dimension of span (x1,x2,x3)

(iv)give a geometric discription of span (x1,x2,x3)

for (i) i solved the matrices

[tex]

\begin{pmatrix}2 & 3 & 2 \\ 1 & -1 & 6 \\ 3 & 4 & 4\end{pmatrix}

[/tex][tex]

\begin{pmatrix}c1 \\ c2 \\ c3\end{pmatrix}

[/tex] = [tex]

\begin{pmatrix}0\\ 0 \\ 0\end{pmatrix}

[/tex]

and i got a not trivial solution which when i let c3=1 i get -4(x1)+2(x2)+(x3)=0

firstly i would like to know if i formed the matrix correctly,should i have put the values accross instead of down?

Thanks

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# Homework Help: Dimensions of span

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