# Quiz: Possibilities For the Solution Set of a Homogeneous System of Linear Equations

## Problem 93

4 multiple choice questions about possibilities for the solution set of a homogeneous system of linear equations.

The solutions will be given after completing all problems.

(The Ohio State University, Linear Algebra Exam)

##### In a Field of Positive Characteristic, $A^p=I$ Does Not Imply that $A$ is Diagonalizable.
Show that the matrix $A=\begin{bmatrix} 1 & \alpha\\ 0& 1 \end{bmatrix}$, where $\alpha$ is an element of a field $F$...