Question 6.7.P.1: Use the inner product axioms to verify the following stateme...

1.\text { By Axiom } 1,\langle v , 0 \rangle=\langle 0 , v \rangle \text {. Then }\langle 0 , v \rangle=\langle 0 v , v \rangle=0\langle v , v \rangle, \text { by Axiom } 3 \text {, so }\langle 0 , v \rangle=0.

2. \text { By Axioms } 1,2 \text {, and then } 1 \text { again, }\langle u , v + w \rangle=\langle v + w , u \rangle=\langle v , u \rangle+\langle w , u \rangle=\langle u , v \rangle+\langle u , w \rangle.