The following three equations define three planes:
Exercise
a) Vary the sliders for the coefficient of the equations and watch the consequences.
b) Adjust the sliders for the coefficients so that

two planes are parallel, the third plane intersects the other two planes,

three planes are parallel, but not coincident,

all three planes form a cluster of planes intersecting in one common line (a sheaf),

all three planes form a prism,

the three planes intersect in a single point.

c) For each case, write down:

the equations,

the matrix form of the system of equations, determinant, inverse matrix (if it exists)