To solve the given system of equations, we can use methods from linear algebra to find the values of [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex]. The given system of equations is:
[tex]\[
\begin{aligned}
5.6x - 2.5y + 1.6z &= 13.06 \\
3.5x + 5.0y - 0.1z &= -6.07 \\
2.1x - 7.5y + 3.2z &= 22.43
\end{aligned}
\][/tex]
After solving this system of equations, the following values are obtained for [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex]:
[tex]\[ x = 0.9 \][/tex]
[tex]\[ y = -1.8 \][/tex]
[tex]\[ z = 2.2 \][/tex]
Thus, the solution set is:
[tex]\[
\{ (0.9, -1.8, 2.2) \}
\][/tex]
So, the correct choice is:
A. There is one solution. The solution set is [tex]\(\{(0.9, -1.8, 2.2)\}\)[/tex].
