Question

Solve each of the following system of homogeneous linear equations.
2x + 3y + 4z = 0
x + y + z = 0
2x − y + 3z = 0

Answer 1

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