Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation \( \mathbf{A x}=\mathbf{b} \). Then solve the system and write the solution as a vector.
\[
A=\left[\begin{array}{rrr}
1 & 6 & -5 \\
-2 & -3 & 1 \\
2 & 3 & 3
\end{array}\right], \mathbf{b}=\left[\begin{array}{r}
7 \\
-5 \\
21
\end{array}\right]
\]
Write the augmented matrix for the linear system that corresponds to the matrix equation \( \mathrm{Ax}=\mathrm{b} \).