Showing That a Function Is Not an Inner Product In Exercises 912, show that the function

Chapter 5, Problem 12

(choose chapter or problem)

Showing That a Function Is Not an Inner Product In Exercises 9 - 12, show that the function does not define an inner product on \(R^{3}\), where \(\mathrm{u}=\left(u_{1}, u_{2}\right)\) and \(\mathrm{v}=\left(v_{1}, v_{2}\right)\).

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

Text Transcription:

R^3

u = (u_1, u_2)

v = (v_1, v_2)

langle u, v rangle = 3u_1 v_2 - u_2 v_1