I must prove the statement below, I believe that I can do this by proof by contradiction. But am I not 100% sure how the contradiction statement should be.
Question Let $\langle \cdot ,\cdot \rangle$ be an inner product. Show that if $\langle x,y\rangle =\langle x,z\rangle$ for all $x$ then $y=z$
My attempt to provide a contradiction statement to prove incorrect:
Let $\langle x,y\rangle =\langle x,z\rangle$ for all $x$ be true but suppose $y\neq z$.
If I did it right then I can pick a value of $x$ that I can use to show why this contradiction will not work, hence proving that $y=z$.