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MANE 3351 - Manufacturing Engineering Analysis

Homework Assignment 6

Assigned: November 13, 2024

Due: November 20, 2024

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 vectors and 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

  1. Find \(\mathbf{A}^T\) (transpose)
  2. Find \(\mathbf{C}^T\) (transpose)
  3. Find \(\mathbf{AB}\) (matrix multiplication)
  4. Find \(\mathbf{AC}\) (matrix multiplication)
  5. Find \(\mathbf{A}^{-1}\) (inverse)
  6. Find \(\mathbf{A}^{-1}\mathbf{A}\)
  7. Find \(\mathbf{B}^{-1}\) (inverse)
  8. Find \(\mathbf{B}\mathbf{B}^{-1}\)

Please upload your submission as a single PDF document to the Homework 6 Drop Box before November 20, 2024.