GATE 2021 EC – Question 26
If the vectors $(1.0,-1.0,2.0)$, $(7.0,3.0,x)$ and $(2.0,3.0,1.0)$ in $\mathbb R^3$ are linearly dependent, the value of $x$ is ________.
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Correct answer: 8
Explanation
Three vectors are linearly dependent when the determinant of the matrix they form is zero. $\begin{vmatrix}1&-1&2\\7&3&x\\2&3&1\end{vmatrix}=1(3-3x)+1(7-2x)+2(21-6)=40-5x=0$, so $x=8$.