Chapter 7.5, Problem 5TFR

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 in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

For any $n\times n$ real, symmetric matrix $A$ and vectors $v$ and $w$ in ${ℝ}^n$, we have $\langle Av,w\rangle =\langle v,Aw\rangle$.