Vectors Linear Dependent?

**Herbststurm** · November 21st 2008, 03:54 AM

Hi

I have to check as this vectors are linear dependent?

My calculation says no, they are linear independent because every coefficient in the linear combination is zero but I don't know as I did my work well. Could you say yer or no to my answer?

The Vectors are in $\mathbb{R}^{4}$

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

**Plato** · November 21st 2008, 05:12 AM

My calculations do not agree with yours.
Try the scalars $\left\langle {\frac{{35}}<br /> {{38}},\frac{{45}}{{38}},\frac{{11}}{{38}}, - 1} \right\rangle$ in that order.
What do you get?

**Herbststurm** · November 21st 2008, 06:50 AM

Hi

okay I tried it and got zero. They are linear dependent. Now I have to search my mistake. Cause I understand what the exercise is, I guess the mistake could be only in the way I solved my linear equation system. The mistake must be in my matrix? Is this correct?

greetings

**Herbststurm** · November 23rd 2008, 03:20 AM

Here is my solution of the linear system of equations. Could you tell me where I did the mistake? I didn't find the problem but it must be wrong because Platos post is true.

Here are my solutions:

Thank you
greetings

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