Answer
a.False
b.False
c.True
d.True
e.True
Work Step by Step
a. False. The trivial solution is always a solution to a homogeneous system of linear equations.
b. False. A nontrivial solution of Ax = 0 is any nonzero x that satisfies the equation. See the
the sentence before Example 2.
c. True. See the paragraph following Example 3.
d. True. If the zero vector is a solution, then b = Ax = A0 = 0.
e. True. See Theorem 6.
