To solve the system of equations in a clean matrix form, we start by rewriting the equations in standard form:
1. \( 5x_1 + 20x_3 = 50 \)
2. \( 10x_2 + 20x_3 = -30 \)
3. \( 5x_1 - 10x_2 = 80 \)
We can express these equations in matrix form \( Ax = b \):
- Coefficient matrix \( A \):
\[
A = \begin{bmatrix}
5 & 0 & 20 \\
0 & 10 & 20 \\
5 & -10 & 0
\end{bmatrix}
\]
- Variable vector \( x \):
\[
x = \begin{bmatrix}
x_1 \\
x_2 \\
x_3