Assignments

1. Let \(A=\begin{pmatrix}1&2&3\\4&5&6\\7&8&10\end{pmatrix}\). Find a matrix X such that \(X\cdot A=\begin{pmatrix}7&8&10\\4&5&6\\1&2&3\end{pmatrix}\). What do you get if you compute \(A\cdot X\)?
2. Find a 4x4 orthogonal matrix with at least 5 non-zero entries.
3. Can you find a 3x3 orthogonal matrix with no zeroes? Notebook
4. Find the vertical edges of a grayscale image (of your choice). Hint: For horizontal edges this is done in Notebook 031.
5. Pick a small grayscale image (your choice) and use matrix transposition and multiplication with suitable matrices to produce the following six images:
6. Problem 3.8
7. Problem 3.16