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Question
Solve each of the following system of homogeneous linear equations.
2x + 3y + 4z = 0
x + y + z = 0
2x − y + 3z = 0
Solution
\[D = \begin{vmatrix}2 & 3 & 4 \\ 1 & 1 & 1 \\ 2 & - 1 & 3\end{vmatrix} \]
\[ = 2 (3 + 1) - 3 (3 - 2) + 4( - 1 - 2)\]
\[ = 8 - 3 - 12\]
\[ = - 7\]
\[\text{ So, the given system of equations has only the trivial solution }i . e . x = 0, y = 0, z = 0\]
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