(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u + v)j + (u? + 3v)k. (a) Find a normal vector to S at the point (3,1,1). (b) Find an equation of the tangent plane to S at (3, 1, 1).
Let V = M2(R), and let U be the span of
S =
2. (a) Let V = M,(R), and let U be the span of s={(1 1) ($ 3). (3), (1 9). (1) 2.)} Find a basis for U contained in S. (b) Let W be the subspace of P spanned by T = {2} + 22 – 1, -2.3 + 2x +1,23 +22² + 2x – 1, 2x3 + x2 +1 -2, 4.23 + 2x2 - -4}. Find...
Problem #5: (a) Let u =(2, -4,-8, -10) and v=(-1, -3, 8, -10). Find ||u – proj,u||. Note: You can partially check your work by first calculating projyu, and then verifying that the vectors projyu and u-proj,u are orthogonal. (b) Consider the following vectors u, v, w, and z (which you can copy and paste directly into Matlab). v = (-8.1 4.2 6.3], w = [-9 -3.7 5.5], u z = = [-8.6 -3.4 -7.1], [-3.2 2 -4.9] Find the...
Find the best approximation to z by vectors of the form C7 V + c2V2. 3 1 3 -1 -6 1 z = V2 4 0 -3 3 1 The best approximation to z is . (Simplify your answer.) - 15 - 8 8 - 1 Let y = , and v2 Find the distance from y to the subspace W of R* spanned by V, and vą, given 1 0 1 - 15 3 3 - 13 09 that...
Question 10 Find the component form of the indicated vector. Let u = {2, -1), v=(-4,-2). Find -4u +5v. (8, 12) 01-28, -3) (12, 14 01-28, -6) Dee
Let u = 5i - j, v = 41+ j, and w=i+6j. Find the specified scalar. u.V+U.W u•v+u•w= (Simplify your answer.) Enter your answer in the answer box. Save for Later < Previous
In R. let V be the orthogonal complement of the vectors u and v, where u = (1,9, 3,61) and v= (4, 36, 13, 254) Find a basis B = {b1,b2} for V: b = 1 Now find five vectors in V such that no two of them are parallel e- LLL
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
DU .U . U U . 1). . . . 20. B={(-3, 2), (8, 4); and B' ={(-1.2), (2,-2); are two bases for R (a) Find the transition matrix from B' to B. (b) Find the transition matrix from B to B'. (c) let [V]8. = [-] find [V]
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Find u + v. u = (5, - 4) and v= (-3, -5) u u+v=< 0) (Simplify your answers.) Use the paralelogram de to find the magnitude of the resultant force for the two foroes shown in the figure. The magrouse of the room force Round on the