Chapter 1.3, Problem 47E

A linear system of the form $A\stackrel{\to }{x}=\stackrel{\to }{0}$ is called homogeneous. Justify the following facts:
a. All homogeneous systems are consistent.
b. A homogeneous system with fewer equations thanunknowns has infinitely many solutions.
c. If ${\stackrel{\to }{x}}_1$ and ${\stackrel{\to }{x}}_2$ are solutions of the homogeneous system $A\stackrel{\to }{x}=\stackrel{\to }{0}$ , then ${\stackrel{\to }{x}}_1+{\stackrel{\to }{x}}_2$ , is a solution as well.
d. If $\stackrel{\to }{x}$ is a solution of the homogeneous system $A\stackrel{\to }{x}=\stackrel{\to }{0}$ and k is an arbitrary constant, then $k\stackrel{\to }{x}$ is a solution as well.