Y1 Y2 ER3 [Y3. (x, y) : 2x1Y1 + x2Y2 + 5x3Y3, for x = X2 ,y = X3 (a) Show that S = is an orthogonal set with respect to the given inner product. Is S an orthonormal set?

Q: Determine if the function defines an inner product on R2, where u = (U₁, U₂) and v= (v₁, v₂).…

A: Define a a function on R² by  ⟨ u , v ⟩ = 8u1v1+u2v1+u1v2+8u2v2 .   Now  Symmetric. ⟨ u , v ⟩ =…

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

Q: Let (u, v) be the inner product on R² generated by A = [ 6 -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find <u, v>

Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

A:

Q: (a) Let be a a- Algebra on X. Assume that , lz: - (0, oo) are two measures on X. Is + kuz a measure…

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

Q: Linear operator T: R2 R2 is defined by T(1,0) (1,4), T(1,1)-(2,2) T one-to-one?

A:

Q: The domain of the functi f (x, y, z) = In(3.xy – 6) {(x, y, z) e R³ : xy 20 {(x, y) € R² : xy 2

A: Consider the function  f(x,y,z)=ln(3xy-6)

Q: 7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3,…

A:

Q: Is the set V = {(x, y) x >0} where (x1, y₁) + (x2, Y₂) = (x₁x2, y₁ + y₂) and c (x, y) = (x,cy) a…

A:

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

A:

Q: Q1. Let u= (1, 1), addition and scalar multiplication on Vas; u+v=(₁+y₁-1, 2+2-1) and a.u = (ay,…

A:

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: Let T : R? → R² such that T (1,0) = (3, 1), and T (0, 1) = (-1,3). Find T (2, 5). T (2, 5)=( (enter…

A:

Q: Which of the following vectors are orthogonal in the Inner Product Space with Inner Product defined…

A: The inner product is defined by .The given vectors are, and .We have to determine whether the…

Q: Consider the vector-valued function [f(x, y) xt – xy² [g(x, y) 2 Vx + y³x² [f(x, y) Which of the…

A: Find the Jacobian of the given matrix

Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

A:

Q: (10) Let the vector space P, has the inner product (p(x), q(x)) = | P(x)q(x)dx (a) Compute ||p(x)||…

A:

Q: Justify wether the following is an inner product or not =5x1y1-x1y2-x2y1+2x2y2 where x=(x1,x1) and…

A: By using axioms of inner product we have to show whether <x, y> is an inner product or not.

Q: True or False: (p, q) = pq defines an inner product on P(R).

A:

Q: Let T:P2(R) → P2(R) T(a + bx + cz?) = 3a – 16 + 6c + ( – 1la + 4b – 22c)z + (– 6a + 36 – 1lc)z? Let…

A: Let us us consider the mapping T:P2ℝ→P2ℝ be defined by Ta+bx+cx2=3a-b+6c+-11a+4b-22cx+-6a+3b-11cx2…

Q: Use the functions f and g in C[-1, 1] to find (f, g), f, g, and d(f, g) for the inner product (f, g)…

A:

Q: Let ((uz,u2,U3),(V1,V2,V))= 2U1V1 + 3u2V2+ U3V3 be an inner product on R, Determine d(1, – 1, –…

A:

Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

A:

Q: 3 4. Let u =-3 and A= 1 1 Is u belongs to the plane in R' spanned by the -6 -2 -8 columns of A? Why…

A:

Q: xy -) zi – xk -) xỉ + zk

A:

Q: of the transformation r = u? + v?, y = 2uv is 9. () The Jacobian 4u? + 4v². a(u,r)

A:

Q: Let (u,v) be the inner product on R² generated by A = = [ and let u = (3, −5), v = (7,4). Find (u,…

A: We have to find