Question:
Solve each of the following system of homogeneous linear equations.
$2 x+3 y+4 z=0$
$x+y+z=0$
$2 x-y+3 z=0$
Solution:
$D=\left|\begin{array}{rrr}2 & 3 & 4 \\ 1 & 1 & 1 \\ 2 & -1 & 3\end{array}\right|$
$=2(3+1)-3(3-2)+4(-1-2)$
$=8-3-12$
$=-7$
So, the given system of equations has only the trivial solution i. e. $x=0, y=0, z=0$
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