Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Linear Algebra Eigenvalues
Which of the following vectors are linearly dependent?
1
\(\left(\begin{array}{l}2 \\ 1 \\ 4\end{array}\right),\left(\begin{array}{l}1 \\ 1 \\ 3\end{array}\right),\left(\begin{array}{l}2 \\ 3 \\ 6\end{array}\right)\)
2
\(\left(\begin{array}{l}1 \\ 1 \\ 3\end{array}\right),\left(\begin{array}{c}1 \\ -1 \\ 1\end{array}\right),\left(\begin{array}{c}-1 \\ 2 \\ 1\end{array}\right)\)
3
\(\left(\begin{array}{l}3 \\ 4 \\ 2\end{array}\right),\left(\begin{array}{c}1 \\ -2 \\ 4\end{array}\right),\left(\begin{array}{c}1 \\ -3 \\ -1\end{array}\right)\)
4
\(\left(\begin{array}{l}1 \\ 2 \\ 1\end{array}\right),\left(\begin{array}{c}2 \\ 1 \\ -4\end{array}\right),\left(\begin{array}{c}-1 \\ 1 \\ 5\end{array}\right)\)