Suppose I have system of 3 equations $$a_1x+b_1y+c_1z=0$$ $$a_2x+b_2y+c_2z=0$$ $$a_3x+b_3y+c_3z=0$$ and cofficient matrix $A=\begin{equation} \begin{pmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{pmatrix} \end{equation}$ So I have been told that solution of this matrix will be non-trivial if $|A|=0$ and trivial in any other case. As far as I know non trivial solution means solutions is not equal to zero but in any case $x,y,z=0$ will satisfy given equations regardless of it's value of determinant. So, why do we call it "non-trivial" solution?
2026-05-14 10:07:46.1778753266
What do trivial and non-trivial solution of homogeneous equations mean in matrices?
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