Answer
Let the n$\times$n matrix $A$ be invertible.
Then, by Th.5 of this section,
for each $\mathrm{b}$ in $\mathbb{R}^{n}$, the equation $A\mathrm{x}=\mathrm{b}$ has the unique solution $\mathrm{x}=A^{-1}\mathrm{b}$.
So, the statement (a) of Th.4 of chapter 1 is valid.
Then, statement (d) of Th.4 is also valid. That is,
The columns of A span $\mathbb{R}^{n}$.
Work Step by Step
The answer contains the explanation, as asked.
