Chapter 4.7, Problem 1TFR

True-False Review

For Questions (a) $—$ (h), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

(a) Every vector in a finite-dimensional vector space $V$ can be expressed uniquely as a linear combination of vectors comprising a basis for $V$.