Answer
The reduced row echelon form of A is I,
to which we apply theorem 4 from section 1.4, and conclude that
$A\mathrm{x} =\mathrm{b}$ has a solution for each $\mathrm{b}.$
Work Step by Step
If $A\mathrm{x}=0$ has only the trivial solution, and A is n$\times$n, a square matrix,
the reduced row echelon form of A is I
(otherwise there would be free variables and solutions other than the trivial one.)
This means that $A$ must have a pivot in each of its rows.
Applying Th.4 from section 1-4, since we have
$\mathrm{d}.\quad A$ has a pivot in each row,
then,
$\mathrm{a}.\quad A\mathrm{x} =\mathrm{b}$ has a solution for each $\mathrm{b}.$
