2005-0.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	0	IB 2005 Linear Algebra	1.I.1C	2005

Let $V$ be an $n$-dimensional vector space over $\mathbf{R}$, and let $\beta: V \rightarrow V$ be a linear map. Define the minimal polynomial of $\beta$. Prove that $\beta$ is invertible if and only if the constant term of the minimal polynomial of $\beta$ is non-zero.