Answer
See below
Work Step by Step
According to Cramer's Rule for a $3\times 3$ system $Ax=b$ where $A=\begin{bmatrix}
a_{11} &a_{12} &... &a_{1n}\\a_{21}& a_{22} & ... &a_{2n}\\a_{n1} &a_{n3}&... & a_{nn}
\end{bmatrix}$ and $b=\begin{bmatrix}
b_1\\b_2\\... \\b_n
\end{bmatrix}$
From the given matrices, we have:
$A=\begin{bmatrix}
3.1 & 3.5 & 7.1 \\2.2 & 5.2 & 6.3 \\ 1.4 & 8.1 & 0.9
\end{bmatrix}\\A_1=\begin{bmatrix}
3.6 & 3.5 & 7.1 \\2.5 & 5.2 & 6.3 \\ 9.3 & 8.1 & 0.9
\end{bmatrix}\\
A_2=\begin{bmatrix}
3.1 & 3.6 & 7.1 \\2.2 & 2.5 & 6.3 \\ 1.4 & 9.3 & 0.9
\end{bmatrix}\\
A_3=\begin{bmatrix}
3.1 & 3.5 & 3.6 \\2.2 & 5.2 & 2.5\\ 1.4 & 8.1 & 9.3
\end{bmatrix}$
We have determinants:
$\det(A)=-44.911\\
\det(A_1)=-169.251\\
\det(A_2)=-29.614\\
\det(A_3)=65.725$
Hence, we have the solutions:
$x_1=\frac{-169.251}{-44.911}=3.769\\
x_2=\frac{-29.614}{-44.911}=0.659\\
x_3=\frac{65.725}{-44.911}=-1.463$
