Determine whether the solution space of the system $Ax = 0$ is a line through the origin, a plane through the origin, or the origin only. If it is a plane, find an equation for it. If it is a line, find parametric equations for it, using $t$ as parameter.
(a) $A = \begin{bmatrix} -1 & 1 & 1 \\ 2 & 4 & 0 \\ -1 & -5 & -1 \end{bmatrix}$
The solution space is a line through the origin
$x = -\frac{2}{3}t$ $y = -\frac{t}{3}$ $z = t$
(b) $A = \begin{bmatrix} 1 & 2 & 3 \\ 6 & 7 & 3 \\ 1 & 0 & 5 \end{bmatrix}$
The solution space is the origin