Answer
When $Ax = 0$ has only the trivial solution, there exists a pivot in each column of $A$. Because there exists a pivot in each column of $A$, we cannot reach multiples of one vector through a linear combination of other vectors. Thus, the solution to $Ax = b$ is unique as we cannot rearrange weights of vectors to achieve $b$.
Work Step by Step
Answer provides full explanation; see answer above.
