- #1
Lynne
- 12
- 0
Homework Statement
Given vectors:
a1 = (1; 2; 0),
a2 = (2; 1; 3),
a3 = (0; 3; -3).
Find out if these vectors are linearly independent.
Homework Equations
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?