# Possibilities of the Number of Solutions of a Homogeneous System of Linear Equations

## Problem 14

Here is a very short true or false problem.

Select either True or False. Then click “Finish quiz” button.

You will be able to see an explanation of the solution by clicking “View questions” button.

## System of linear equations

Determine whether the following sentence is True or False.

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##### Common Eigenvector of Two Matrices and Determinant of Commutator

Let $A$ and $B$ be $n\times n$ matrices. Suppose that these matrices have a common eigenvector $\mathbf{x}$. Show that $\det(AB-BA)=0$.

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