7.2: Introduction to Gauss Jordan Elimination
- Page ID
- 63901
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The following elementary row operations
- Interchange two rows of a matrix
- Multiply the elements of a row by a nonzero constant
- Add a multiple of the elements of one row to the corresponding elements of another
Consider the element \( a_{2,1} \) in the following \( A \) Matrix.
\[ A = \left[
\begin{matrix}
1 & 1 \\
20 & 25
\end{matrix}
\, \middle\vert \,
\begin{matrix}
30 \\
690
\end{matrix}
\right] \nonumber \]
Describe an elementary row operation that could be used to make element \( a_{(2,1)} \) zero?
What is the new matrix given the above row operation.
Modify the contents of this cell and put your answer to the above question here.
\[ A = \left[
\begin{matrix}
1 & 1 \\
0 & ??
\end{matrix}
\, \middle\vert \,
\begin{matrix}
30 \\
??
\end{matrix}
\right] \nonumber \]
The following function is a basic implementation of the Gauss-Jorden algorithm to an (m,m+1) augmented matrix: