3. Prove that the set S = { co COS ηπχ ,sin ηπχ : n = 1, 2, 3, ...} is orthogonal in PC[-L, L]. 4. Is the set S an orthonormal set in PC[-L, L]? How do you know?

Q: Ex:@ Suppose thet the tallowing transformutioun Conneciãs the (x') and (xi) cordnate ار ک هأولاS…

A: Question: The transformation is T=x¯1=ex1+x2x¯2=ex1-x2 Calculate: (1) The jacobian matrix J and J-1…

Q: 7. Consider the set of real numbers A= [x:0 <x<1]U (2) in R'. Describe A for the following…

A: Solution

Q: (2,3) is te i చాంబ! Under a ro dediona Identidy three distinct point that Cald be the center & of

A:

Q: 7) T (u, ) -(υ, 2 cos u, 4sin u). Consider the parameterization With 0, y ve (1,3]. u € describing…

A: Direction of normal always positive y axis. So y component of the normal is positive.

Q: 2 5. Given vectors, vị = , V2 = • V3 = use Gram-Schmidt to fine a corresponsding orthonormal set…

A:

Q: The value of cos8n from the unit circle is (0,1) t (1,0) (-1,0) (0,-1) a) 0 b) 1 c) – 1 d) undefined…

A: Folow 2nd step.

Q: 2. Determine the equation of the following function. State your answer as a piecewise function. y 10…

A:

Q: distance Q.2A) ((q,x+ 92y+ 93z = M, ,41x + 92y+932 = M2)) |M, – M2| Prove the between to planes…

A: Let the point (x1,y1,z1) is on plane 1 and the point (x2,y2,z2) is on plane 2. As we already know…

Q: 1. By using the standard metroie X. Determine JA and X\A. Justify your answer. State whether A is…

A:

Q: Let P = X(XX) X'. and Q = I-P. Prove that (a) and idempotent. (b) QX=0 and X'Q=0. I and Q are…

A:

Q: Q4/ Describe the following sets: {z: e²=i}, {z: e² = -1}, {z: e² = - i}, {z: cos z = 0}, {z: sin z =…

A:

Q: Please solve 4,5,6,7 The Borel o-algebra on Ris generated by any of the following collections of…

A: As per the company policy, in a multipart question like this, we can solve only the first two…

Q: Determine if u and v u = (cos 0, sin 0,–1); v= (sin 0.-cos 0,0) are orthogonal

A: We have to determine if u and v are orthogonal   The given vectors are u=cosθ, sinθ, -1v=sinθ,…

Q: b) Use chain rule 1 y= LESANNE aretan u where u eª ue

A:

Q: У ,ーテ = ,-, + テ-テ - y = y: ij ij i. i. and (y;-y 10, – 7,) + 6, - 7) | ij ij i. ーリ-bー)+G.-) 2 2 2…

A:

Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: 3. Let X = {a,b,c ,d, e}, f ={{a,b}.{b.c}.fc.e}.fe}}cP(X) Find the topology z on X generated by B.

A:

Q: Suppose ū (5, 3, 0) and v = (3, 1, –1). The projection of ū along ở is

A:

Q: 4. Is the set S an orthonormal set in PC[−L, L]? How do you know?

A: To check if a given set of vectors is orthonormal, we need to check two conditions: Orthogonality:…

Q: 1 Properties of the Cross Product: lamat, 1.) ||lox b|| = |lo||-·||bl| - sind, where O & [alt] is…

A: As this question has multiple subparts, hence only first five subparts will be done.

Q: COS C30) =4 CCOSO) 3_ 3cos CG)

A:

Q: [2,5]U[3, 7]=[2,7]. (1,3)^(3,5) = 0.

A:

Q: If H is a subgraph of G, then show that dg(u,v) <dí(u,v).

A: A graph G illustrates how the vertices and edges are connected. Thus a graph is an ordered pair…

Q: Let w where z = rei0. 1) Show that by using Cauchy Riemann Equation (C.R. Eq.) in polar form that w…

A:

Q: 14. (T/F) Given S = {b.....bx) in R", each p in aff S has a unique represcntation as an affine…

A: Note:- As per our guidelines, we can answer the first one as all the  are not subpart of a…

Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: 15. Suppose that a, b e Z and gcd(a, b) = 1. Prove that ged(a", b") = 1 for m, ne N. N and lot 8 frm…

A:

Q: iven that use the bhi tzS to compute %3D irst shifting Theorem [e"e cos 7+]

A:

Q: 1 M8. The projection of u= onto = is given by 3 1 3 1/2 3 3 A. C. D. 1 E. 3 0. 3/2 B.

A: As we know that the expression for the vector projection of u→ onto v→ is: projvu=v·uv2v Given:…

Q: 7 the n ya In Cx? _y?) Do not Equatio InCx-yリ Do not check modificd Laplace

A: This is a problem of partial and Laplace.

Q: QUESTION 16 Use the funesions f0)=x" nd góv) =x +1 n C-1, 1] to find 4. g) for the inne produca (.…

A: Option (c) is true.

Q: true or false without justify The sel { 1,2,t, 3,,4,+, csx, coss is mot Ti Bomded in (CToi], Ul6)…

A: True.

Q: 3) le w= u(x,y)+ iv(xiy) and I=X+ a) for function w show the providing the condition of Vu. Vv =O…

A: Since you have asked for a multiple question , we will solve the first question for you. If you want…