Inner Products

Inner Product Spaces Exercise 1 In each part, determine whether the set of vectors is orthogonal and whether it is orthonormal with respect to the Euclidean inner product on ℝ². $ (0, 1), (2, 0) $ $(- \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}), (\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ $(- \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}), (\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$ $ (0, 0), (0, 1) $ Exercise 2 In each part, determine whether the set of vectors is orthogonal and whether it is orthonormal with respect to the Euclidean inner product on $\mathbb{R}^2$. ...

Inner Products Exercise 1 Let $\mathbb{R}^2$ have the weighted Euclidean inner product: $$ \langle u, v \rangle = 2u_1v_1 + 3u_2v_2 $$and let $u = (1, 1)$, $v = (3, 2)$, $w = (0, -1)$, and $k = 3$. Compute the stated quantities. $ \langle u,v \rangle $ $ \langle ku,w \rangle $ $ \langle u+v , w \rangle $ $ | v | $ $ d\langle u,v \rangle $ $ | u-kv | $ Exercise 2 Let $\mathbb{R}^2$ have the weighted Euclidean inner product: ...