2014-37.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	37	IB 2014 Linear Algebra	Paper 2, Section I, G	2014

State and prove the Rank-Nullity Theorem.

Let $\alpha$ be a linear map from $\mathbb{R}^{5}$ to $\mathbb{R}^{3}$. What are the possible dimensions of the kernel of $\alpha$ ? Justify your answer.