\[\begin{matrix} a_1x& +&a_2y&+&a_3z&=&0\\ b_1x & +&b_2y&+&b_3z&= &0\\ c_1x&+&c_2y&+&c_3z&=&0 \end{matrix}\]
What can be said about the vectors \(\begin{bmatrix}a_1\\b_1\\c_1\end{bmatrix}\), \(\begin{bmatrix}a_2\\b_2\\c_2\end{bmatrix}\) and \(\begin{bmatrix}a_3\\b_3\\c_3\end{bmatrix}\)?
Select all that apply.
Nothing can be deduced from the information given. The three vectors are linearly independent. The three vectors are
linearly dependent. The three vectors are pairwise orthogonal. The first vector can be written as a linear combination of
the other two. The equation \(\alpha \begin{bmatrix}a_1\\b_1\\c_1\end{bmatrix}+\beta \begin{bmatrix}a_2\\b_2\\c_2\end{bmatrix}+\omega \begin{bmatrix}a_3\\b_3\\c_3\end{bmatrix}=\vec {0}\) has only the trivial solution.