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

Problems and solutions in Linear Algebra

Problem 14

Here is a very short true or false problem.

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

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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 $\det(AB-BA)=0$.