Let D be the portion of z px + qy +r over a region in the xy plane that has area A, oriented up, and let F = (ax + by + cz)i+ (ax + by + cz)j+(ax + by + cz)k. Compute F. dr. ae Select one: a. A(p(c+b)+q(a-c)+a-b) b. Non of them с. А(p(с-b)+q(a-с)+a-b)

Q: Let Z = (1, 1, 2) be a point in R³. Find the closest point to Z tha lies on the plane give by -x+y-z…

A: The normal vector to the plane is <-1, 1, -1>. The point you seek would have to be some…

Q: 4. Check that the following are vector spaces: (a) RN. 55 / 600 (b) CN. (c) C(N), where 2 is a…

A: A non-empty set V, +, · is said to be a vector space over a field F together with operations of…

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: show thal the set of all poiuts in the Subspace of IR 3. plane ax +by+CZ =0 is +cz = ois CA

A:

Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: 22Prove that the line X2l+2t y=ー+3t そ2 :2+4t is s perpendicular tou the plane X-2yrzz6

A:

Q: Consider the vector space R³ and d₂(x, y) = (-1lx - y²). Show that d₂ satisfy M3 (The tringle…

A: Consider the vector space We  have  to prove triangle  inequality   that  is  we  have to how that…

Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: 2) One of the following subsets of IR2 is not subspace: a) S = {, xeR} b) s = {], = x3} %3D %3D e) s…

A:

Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

A:

Q: b.) show that IR³ - W₁ + W₂. t C.) Find a subspace V such that IR³ =W₁ U.

A:

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: Show that V={(x,2020x): x in R} is a vector space

A: According to the given information, it is required to show that the given set is a vector space.

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

A:

Q: What is the dimension of the subspace H of R? spanned by 2 -4 4 32- :? -5 10 -10 O A) 0 O B) 3 O ) 4…

A: The number of vectors in a basis of a vector space is said to be the dimension of that vector space…

Q: Find the distance from y to the plane in R³ spanned by the set (U₁, U₂} 6 - 2 4 y = -9 a. b. C. 43₁…

A:

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

A:

Q: Let v= C[-1,1] What is the norm of the functionf(x) = - x in this space? O A) 2V5 O B) 2V10/5 OC)…

A: An inner product in the vector space of continuous functions in [-1, 1], denoted asV=C-1, 1, is…

Q: Is every liner operator T : IR2 → IR2 diagonalizable? Justify!

A: Linear transformation and diagonalization

Q: Let vi # v2 E R" and define W1 Span{v2}. Use the definition to show W+n W, is a subspace of R".…

A:

Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

A: