Classify and reduce the relation y²u- 2xyuy + x²u,y ="u, + =u, to a canonical form and. %3D olve it.

Q: Q:05 that the dual Space Show Co is of

A: The dual of c0  is l1  Let f=( f(1),f(2),f(3),...) ∈c0 and g=(g(1),g(2),g(3),...)∈l1.then  we claim…

Q: Part (A): Recall that VA, B C U: (A = B): → (36 € Fnc(A,B)(Bij($))). Prove that (=) is an…

A: a) Given -∀A , B ⊆ μ : ( A ≃ B ) : ⇔∃ϕ ∈ Fnc(A,B)(Bij(ϕ)) To prove - ≃ is an equivalence relation on…

Q: (b) Let R = {(x, y) E R × R : 1 < ¤ < 4 or x = 6}, and S = {(x, y) E R × R : -1 < y < 1}. i. Find…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

Q: 7. State the congruence relation for ABWO and AIRO. Use only the markings in the diagram. A. ASA B.…

A: As per our guidelines we are suppose  to solve only first question. Kindly repost the other question…

Q: Let →a=⟨3,1⟩ and →b=⟨1,0⟩. Find the projection of →b onto →a. proj→a →b=

A:

Q: Let G = &lt;x, y | x8 = y2 = e, yxyx3 = e&gt;. Show that |G| ≤ 16. Assuming that |G| = 16, find the…

A:

Q: Let A = {6, 9} , R relation on A defined R by. %3D R = {(a, b): a +2 = b -1 ,a, b E A}. Write R. %3D

A:

Q: Determine the image of the line Im(z) = -2 under the mapping f(z) = i(7 )? and describe it in words

A: Find the image of the line Imz=-2 under the mapping fz=iz2. Let w=fz, and write w=u+iv,   and…

Q: Exercise 2. Which of the following maps o : (a) $(r, y) = (x², r*, y) %3D

A: Please find the sol in next step, Shall we solve one question only as you have asked more than one…

Q: A. Let R be a relation on set A. A={x :xeJ and 0 sx s 12), and R={(a,b) : la - b| is multiple of 4}.…

A: Since not particular question asked, as per guidelines solution to only first question(i.e A) is…

Q: b- Let X₁, X2,.... Xn b (a) Find a complete (b) Find the UMVU

A: Solution:   (a):

Q: Let f be the map Sanding each complex pumber Show that fl.z)-f2)f(2)

A:

Q: The notation (x, y) (y, x) defines a reflection in the coordinate plane. O True O False QuickNa

A:

Q: Q/ show thet f(2) = 2+ Conformal maps 121= 1 ? on

A:

Q: Define a map t: R × R → R × R by t(a, b) = (a+ b, a - b). Prove that t is a one-to-one…

A: The solution is given as

Q: IS a function.. (b) Let R= {(x,y) € R × R : 1 < ¤ < 4 or x = 6}, %3D and S = {(x, y) E R × R : –1 <…

A:

Q: ent, find a linear relation. a) vi = (2, 1, 0), V2 = (0, 1,0), V3 = (-1,2,0) %3D b) wi = (1,2, –2),…

A:

Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

A:

Q: Form PDE by eliminating arbitrary tunction m the relation Ø(x² + y² + z²,z² – xy) = 0

A:

Q: R. I relations on A.

A:

Q: 4. Classify and reduce the following equations to a canonical form: (a) yu -x*u, = 0, x>0, y>0. (b)…

A: To classify and reduced in canonical form of the given equation is..

Q: Reduce to Canonical form y² Ur – 2 y Ury+ Uyy = Uz + 6 y O Um = 0

A:

Q: Let a = ( – 3, 4) and b = ( – 3, 1). %3D | %3D Find the projection of b onto a. projā b %3D

A:

Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

A:

Q: Let T : R3 → R² be a linear mapping. 2 .T Given that T and T find T

A:

Q: Questron 5. Check whether the relation R in R defined by R = {(a, b): a < b³} is reflexive,…

A:

Q: The transformation T: R? - R', T|a b=[a - 8a). -a is linear ulgn O Ind.

A: See solution below

Q: Let ū = 2i – k and ī = i+3j + k. Compute |ū], |T], ū x ī, and Projzū.

A: Solution is here

Q: 5. Let U and V be the relations in R defined by U={(x,y):x² +2y=5} and ={(x,y):2x-y=3}. a) Find VoU.…

A:

Q: Below are four coordinate axes for 3-space, labeled I, II, III, and IV. Which sets of axes adhere to…

A: Once the x- and y-axes are specified, they determine the line along which the z-axis should lie, but…

Q: Prove or disprove whether the function f (r) = a +2 is a bijection from R R %3D

A:

Q: Define the linear transformation T : R? R' by T(x) = Ax. Find the images of u = and u under T

A:

Q: .The table below shows corresponding values of x and y which approximately satisfy a relation of the…

A:

Q: Describe conditions on v = [a, b, c]² such that u x v = 0 where u = [1, 2, 3]ª and 0 is the

A: Vector multiplication problem....

Q: a Let R = . b DeZ and let o: R→Z be a mapping defined by: b = a-b. b a

A:

Q: Use Green's Theorem to evaluate F dr, where F(2, y) = (9xy, y" - 8) and C is the rectangle with…

A: That's easy. Have a great day!!!

Q: Define to mapping pi : R2(arrow)R by pi((x,y)) = x. Find the kernel of pi.

A:

Q: a Let R = b beZ}and let o: R→ Z be a mapping defined by : b |= a-b. b a

A: Ring homomorphism

Q: Find the Jacobian ∂(x,y) ∂(u,v) for the transformations x=4ucos(6v)​, y=4usin(6v) and x=4usin(6v)​,…

A:

Q: (b) Let R= {(x, y) E R × R : 1 < x < 4 or x = 6}, and S = {(x,y) E R × R : –1< y < 1}. i. Find the…

A: Solution: The given relations are R=x,y∈ℝ×ℝ : 1≤x≤4 or x=6 and S=x,y∈ℝ×ℝ : -1&lt;y&lt;1

Q: If v = (v1, v2) and T(v)=v except T(0, v2) = (0, 0) then T(v + u) = T(v) + T(u) showing that the…

A: Linear with respect to addition is given. We have to prove for scalar multiplication.

Q: Determine the image of the set S under the given complex mapping w = f(z). i) f(z) = 7 ; S is the…

A: We have the complex mapping : w=f(z)f(z)=z¯ S is the line y=x Let x=t , then y=t Let, z=x+iy…

Q: Let f be the map sending each complex number z-> Show that, f/2,22)e flzi);f(z2)

A:

Q: LeA R be the relation defined the se4 Nx Z that (xy)EIC on so if and only if a) What is. the domain…

A:

Q: followings

A:

Q: The adjacency matrix for the relation R on {v1, v2, v3, V4} is given below. 1 0 1 1 0 0 1 1 1 1 1 1…

A: Given the adjacency matrix for the relation R on the set A=v1, v2, v3, v4 as,…