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Math Help - Vectors Linear Dependent?

  1. #1
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    Vectors Linear Dependent?

    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}
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  2. #2
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    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?
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  3. #3
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    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
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  4. #4
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    Where is the mistake in the system of linear equations?

    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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