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Suppose that f(x,y), x(u,v) and y(u,v) define differentiable functions on all R2 and let g(u,v)= f(x(u,v),y(u,v )). Apply the chain rule to complete the tables, according to the data given in them.
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- Find u · v, u· u, ||v|2, (u · v)v, and u · (3v). u = (2, 12), v = (-3, 2) (a) u. v (b) u.u (c) ||비2 (d) (u· v)v (e) u: (3v)Find u - v, 2(u + 3v), and 2v u. u-(6, -8, 5, 3), v= (-2, 블-글 -1) (a) u- v = = (b) 2(u + 3v) = (c) 2v – u =Find ||u|, u = (-1, 4), v = (4, 5) (a) ||u|| (b) (c) |v||, u v, and d(u, v), (d) ||v|| U V d(u, v)
- Find u · v, u· u, ||v||², (u - v)v, and u · (3v). u = (3, 12), v = (-2, 3) (a) u. V (b) u. u (c) (d) (u . v)v (e) u. (3v)Find u v, uu, ||u||2, (u v)v, and u. (2v). . u = (5,-8, 8), v = (-6, -1, 2) (a) u v (b) (c) (d) (e) U U ||u||² (u . v)v u. (2v)3 3 3 -1 2 V1 = 2 4 V2 and v3 %3D -1 1 1 4 Use the Gram-Schmidt procedure to produce an orthogonal set with the same span. (Hint: If you have unlimited submissions, it might be useful to submit to check your answer for each vector u; before continuing.) The u; must be given in the same order as provided by the standard procedure. Uj =
- Find u v, u u, ||v||², (u · v)v, and u · (3v). u = (3, 10), v = (-4, 3) (a) u• V (b) u u (c) ||v| (d) (u· v)v (e) u (3v)Find u · v, u · u, ||v||2, (u - v)v, and u · (3v). u = (3, 11), v = (-4, 3) (a) u: v (b) u.u (c) ||v||2 (d) (u· v)v (e) u. (3v)Find u · v, u · u, ||v||2, (u · v)v, and u · (3v). u = (2, 10), v = (-3, 2) (a) u v (b) U U (c) V² (d) (u v)v (e) u (3v)
- What are the coordinates of W ()? (0, 1) (-물물) * 12* (-1, 0) * 0, 2x (1, 0) 13 ( "(물,골) 17 3 (0, -1) 02018 Gynlyon, ho. ㅇ (0, 1) ㅇ(을, 물) °(-을, 몰) ° (}, 4)Find u · v, v· v, ||u ||², (u · v)v, and u · (5v). u = (-3, 4), v = (3, 2) (a) u. v (b) v. v (c) (d) (u· v)v (e) u. (5v)Find u · v, u· u, ||v ||2, (u · v)v, and u · (3v). u = (2, 11), v = (-5, 2) (a) u: v (b) u u (c) ||v||2 (d) (u · v)v (e) u· (3v)