Homogeneous Linear systems$A\mathbf{X}=\mathbf{0}$ always has at least one solution $\mathbf{X}=\mathbf{0}$. (Trivial Solution) if and only if the equation has at least one free variables(infinitely many solutions): Nontrivial Solution Ex. Determine whether there is a nontrivial solution.$$\left\{\begin{matrix}3x_1+5x_2-4x_3=0 \\ -3x_1-2x_2+4x_3=0 \\ 6x_1+x-2-8x_3=0 \end{matrix}\right. $$ So..
