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

$$\begin{gathered} D=\left|\begin{array}{ccc}2& 3& 4\\ 1& 1& 1\\ 2& -1& 3\end{array}\right| \\ =2(3+1)-3(3-2)+4(-1-2) \\ =8-3-12 \\ =-7 \\ \mathrm{So},\mathrm{the}\mathrm{given}\mathrm{system}\mathrm{of}\mathrm{equations}\mathrm{has}\mathrm{only}\mathrm{the}\mathrm{trivial}\mathrm{solution}\mathrm{i}.\mathrm{e}.\mathrm{x}=0,\mathrm{y}=0,\mathrm{z}=0 \end{gathered}$$