Question

A weighted Euclidean inner product on $R^{2}$ is given for the vectors $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right) .$ Find a matrix that generates it. $$\langle\mathbf{u}, \mathbf{v}\rangle=4 u_{1} v_{1}+6 u_{2} v_{2}$$

          A weighted Euclidean inner product on $R^{2}$ is given for the vectors $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right) .$ Find a matrix that generates it.
$$\langle\mathbf{u}, \mathbf{v}\rangle=4 u_{1} v_{1}+6 u_{2} v_{2}$$

Added by Austin V.

Linear Algebra and Its Applications

David C. Lay, Steven R. Lay, Judi J.… 5th Edition

Instant Answer

Solved by Expert Likhit Ganedi

11/28/2021

Step 1

Step 1: To generate the weighted Euclidean inner product on $\mathbb{R}^{2}$ given by $\langle\mathbf{u}, \mathbf{v}\rangle = 4u_{1}v_{1} + 6u_{2}v_{2}$, we need to find the matrix $A$ that generates it. Show more…

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A weighted Euclidean inner product on $R^{2}$ is given for the vectors $\mathbf{u}=\left(u_{1}, u_{2}\right)$ and $\mathbf{v}=\left(v_{1}, v_{2}\right) .$ Find a matrix that generates it. $$\langle\mathbf{u}, \mathbf{v}\rangle=4 u_{1} v_{1}+6 u_{2} v_{2}$$