Question
Find a matrix that generates the stated weighted inner product on $R^{2}$.$$\langle\mathbf{u}, \mathbf{v}\rangle=2 u_{1} v_{1}+3 u_{2} v_{2}$$
Step 1
This can be written in matrix form as $\mathbf{u}^{T}A\mathbf{v}$, where $A$ is the matrix that generates the weighted inner product. Show more…
Show all steps
Your feedback will help us improve your experience
Wendi Zhao and 64 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
Find a matrix that generates the stated weighted inner product on $R^{2}$. $$\langle\mathbf{u}, \mathbf{v}\rangle=\frac{1}{2} u_{1} v_{1}+5 u_{2} v_{2}$$
Inner Product Spaces
Inner Products
Find a matrix that generates the stated weighted inner product on $R^{2}$. $$\langle\mathbf{u}, \mathbf{v}\rangle=2 u_{1} v_{1}+3 u_{2} v_{2}$$
Express the matrix $A$ as a product of elementary matrices. $$A=\left[\begin{array}{rrr}0 & -4 & -2 \\1 & -1 & 3 \\-2 & 2 & 2\end{array}\right]$$
Matrices and Systems of Linear Equations
Elementary Matrices and the LU Factorization
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD