Find a homogeneous linear system of two equations in three
unknowns whose solution space consists of those vectors in IR³ that
are orthogonal to $\vec{a} = (-3, 2, -1)$ and $\vec{b} = (0, -2, -2)$.
What kind of geometric object is the solution space?
Find a general solution of the system obtained in part i., and confirm
that Theorem 3.4.3 of the textbook holds.
THEOREM 3.4.3 If A is an m x n matrix, then the solution set of the homogeneous
linear system $Ax = 0$ consists of all vectors in $R^n$ that are orthogonal to every row
vector of A.
