MANE 3351 - Manufacturing Engineering Analysis
Homework Assignment 7
Assigned: November 24, 2025
Due: December 1, 2025 (no late submissions)
Homework 7 covers solving systems of equations using row echelon form, Gauss-Jordan Elimination with pivoting and find matrix inverse using Gauss-Jordan Elimination (with pivoting) by hand. Please work all problems by hand; copying output from Python will not help you on the final exam. Please note that all questions may not have mathematical solutions. If the solutions does not exist or is not defined, state this in your answer. You will use the following matrices in this assignment.
\[
\mathbf{A}=\begin{bmatrix}1.0 &10.0 \\ 2.0&5.0\end{bmatrix}\nonumber
\]
\[
\mathbf{B}=\begin{bmatrix}23.2 & 4.4 &89.4\\93.4&9.3&9.1\\34.2&5.4&8.2\end{bmatrix}\nonumber
\]
\[
\mathbf{C}=\begin{bmatrix}9.4&2.0&8.2\\5.2&7.5&2.1\end{bmatrix}\nonumber
\]
\[
\mathbf{a}=\begin{bmatrix}4\\5\end{bmatrix}\nonumber
\]
\[
\mathbf{b}=\begin{bmatrix}1\\2\\3\end{bmatrix}\nonumber
\]
Questions
- Find \(\mathbf{A^{-1}}\) using Gauss-Jordan Elimination with partial pivoting,
- Solve \(\mathbf{Ax=a}\) using Gauss-Jordan Elimination with partial pivoting, and
- Solve \(\mathbf{Bx=b}\) using row echelon form with backwards substitution. Note this question does not require reduced row echelon form or partial pivoting.
Please upload your submission as a single PDF document to the Homework 7 Drop Box before December 1, 2025.