Elements of Numerical Mathematical Economics with Excel

Exercises

1. Solve the following linear system using the Excel Solver, the inverse, and the Cramer rule:
$[\begin{matrix} 1 & 1 & 1 \\ 2 & 3 & - 1 \\ 7 & 1 & - 2 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 9 \\ 16 \\ 57 \end{matrix}] .$
Resorting to the Rouché–Capelli theorem, analyze whether the system admits only one solution or not.
2. Solve the following linear system using the Excel Solver, the inverse, and the Cramer rule:
$[\begin{matrix} 2 & 1 & 4 \\ 3 & 2 & 1 \\ 1 & 3 & 3 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}] = [\begin{matrix} 16 \\ 10 \\ 16 \end{matrix}] .$
Resorting to the Rouché–Capelli ...

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