MANE 3351 - Manufacturing Engineering Analysis
Homework Assignment 6
Assigned: November 17, 2021
Due: November 30, 2021
Homework 6 covers matrix operations 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 \(\mathbf{A}^T\) (transpose)
- Find \(\mathbf{C}^T\) (transpose)
- Find \(\mathbf{A}^{-1}\) (inverse)
- Find \(\mathbf{A}^{-1}\mathbf{A}\)
- Find \(\mathbf{B}^{-1}\) (inverse)
- Find \(\mathbf{B}\mathbf{B}^{-1}\)
- Solve \(\mathbf{Ax=a}\) by forming an augmented matrix and using row echelon form with backwards substitution (Gauss Jordan Elimination)
- Solve \(\mathbf{Bx=b}\) by forming an augmented matrix and using row echelon form with backwards substitution (Gauss Jordan Elimination).
Please upload your submission as a single PDF document to the Homework 6 Drop Box before November 30, 2021