10.2: Generalize the procedure

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We are going to think about Gauss-Jordan as an algorithm. First I want you to think about how you would generalize the procedure to work on any matrix. Do the following before moving on to the next section.

Do This

Use the following matrix to think about how you would solve any system of equations using the Gauss-Jordan elimination algorithm. Focus on the steps.

\[\begin{split}
\left[
\begin{matrix}
a & b & c \\
e & f & g \\
i & j & k
\end{matrix}
\, \middle\vert \,
\begin{matrix}
d \\ h \\ l
\end{matrix}
\right]
\end{split} \nonumber \]

Question

What are the first three mathematical steps you would do to put the above equation into a reduced row echelon form using Gauss-Jordan method?

Pseudocode

Question

Write down the steps you would complete to implement the Gauss-Jordan elimination algorithm as a computer programer. Some questions to answer:

What are the inputs?
What are the outputs?
How many and what types of loops would you have to guarantee success of your program?

Once you have thought this though the instructor will work with you to build the algorithm.