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

Given vectors:

a1 = (1; 2; 0),

a2 = (2; 1; 3),

a3 = (0; 3; -3).

Find out if these vectors are linearly independent.

2. Relevant equations

3. The attempt at a solution

[tex]

\begin{cases}

\lambda_1+2\lambda_2=0;\\

2\lambda+\lambda_2+3\lambda_3=0;\\

2\lambda_2-3\lambda_3=0;\\

\end{cases}\\

\lambda_1=\lambda_2=\lambda_3=0

[/tex]

[tex]

D=\begin{vmatrix} 1 & 2 & 0 \\ 2 & 1 & 3 \\ 0 & 3 & -3 \end{vmatrix}=0

[/tex]

Vectors are not linearly independent because determinant is zero.

Am I correct?

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# Homework Help: Linearly independent vectors (simple question)

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