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which one of w1 or w2 linear independent of the v groupr??

i got to the situation that each one of them could be independant and the other not

??

the answer in the book is that w2 is independent and the other is not

[tex]

v_1=\begin{bmatrix}

1\\

1\\

-2\\

1

\end{bmatrix}

v_2=\begin{bmatrix}

3\\

0\\

4\\

-1

\end{bmatrix}

v_3=\begin{bmatrix}

-1\\

2\\

5\\

2

\end{bmatrix}

w_1=\begin{bmatrix}

8\\

-10\\

18\\

-14

\end{bmatrix}

w_2=\begin{bmatrix}

3\\

4\\

1\\

1

\end{bmatrix}

[/tex]

http://img147.imageshack.us/img147/8002/64728417.th.gif [Broken]

i got to the situation that each one of them could be independant and the other not

??

the answer in the book is that w2 is independent and the other is not

[tex]

v_1=\begin{bmatrix}

1\\

1\\

-2\\

1

\end{bmatrix}

v_2=\begin{bmatrix}

3\\

0\\

4\\

-1

\end{bmatrix}

v_3=\begin{bmatrix}

-1\\

2\\

5\\

2

\end{bmatrix}

w_1=\begin{bmatrix}

8\\

-10\\

18\\

-14

\end{bmatrix}

w_2=\begin{bmatrix}

3\\

4\\

1\\

1

\end{bmatrix}

[/tex]

http://img147.imageshack.us/img147/8002/64728417.th.gif [Broken]

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