Problem_1

\begin{eqnarray}
\left\{
x_{1}= \frac{1}{D} \left[ D_{1,1}b_{1}-D_{2,1}b_{2}+\dots+(-1)^{n+1}D_{n,1}b_{n} \right] \nonumber \\
\cdots \nonumber \\
x_{k}= \frac{1}{D} \left[ (-1)^{k+1}D_{1,k}b_{1}+(-1)^{k+2}D_{n,2}b_{2}+\dots+(-1)^{k+n}D_{n,k}b_{n} \right] \\
\dots \dotfill \dots \nonumber \\
x_{n}= \frac{1}{D}= \left[ (-1)^{n+1}D_{n,1}b_{1}+(-1)^{n+2}D_{n,2}+\dots+D_{n,n}b_{n} \rigt] \nonumber
\right
\end{eqnarray}