Showing That a Function Is Not an Inner Product In Exercises 1316, show that the

Chapter 5, Problem 16

(choose chapter or problem)

Showing That a Function Is Not an Inner Product In Exercises 13-16, show that the function does not define an inner product on \(R^{3}\), where \(\mathrm{u}=\left(u_{1}, u_{2}, u_{3}\right)\) and \(\mathrm{v}=\left(v_{1}, v_{2}, v_{3}\right)\)

\(\langle\mathbf{u}, \mathbf{v}\rangle=2 u_{1} u_{2}+3 v_{1} v_{2}+u_{3} v_{3}\)

Text Transcription:

R^3

u = (u_1, u_2, u_3)

v = (v_1, v_2, v_3)

langle u, v rangle = 2 u_1 u_2 + 3 v_1 v_2 + u_3 v_3