Question
Show that the function defines an inner product on $R^{2},$ where $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right)$$$\langle\mathbf{u}, \mathbf{v}\rangle=\frac{1}{2} u_{1} v_{1}+\frac{1}{4} u_{2} v_{2}$$
Step 1
Step 1: We need to show that the function $\langle\mathbf{u}, \mathbf{v}\rangle=\frac{1}{2} u_{1} v_{1}+\frac{1}{4} u_{2} v_{2}$ satisfies the properties of an inner product. Show more…
Show all steps
Your feedback will help us improve your experience
Ahmad Reda and 51 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Show that the function defines an inner product on $R^{2},$ where $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right)$ $$\langle\mathbf{u}, \mathbf{v}\rangle= 2 u_{1} v_{2}+u_{2} v_{1}+u_{1} v_{2}+2 u_{2} v_{2}$$
Inner Product Spaces
Show that the function defines an inner product on $R^{2},$ where $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right)$ $$\langle\mathbf{u}, \mathbf{v}\rangle= 3 u_{1} v_{1}+u_{2} v_{2}$$
Show that the function defines an inner product on $R^{2},$ where $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right)$ $$\langle\mathbf{u}, \mathbf{v}\rangle= u_{1} v_{1}+9 u_{2} v_{2}$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
