Let E = Q(V2,v3,V5). (1) Find 3 distinct non-trivial elements in Aut(E/Q). (2) Denote such three by o, t, 8. Find Eo, Et , ES, AND E{o, t}, E{o, 8}, E{t, 6}, E{o, T, 6}.

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: HW_2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 < Z < 2) c) p(-2 < Z < 1)

A: Solution

Q: 3. If A = {1, 2} and B = {x, y}, then AXB = O {1,x), (1,y), (2,x), (2,y)} O {1,x), (2.y)} none of…

A: We have to solve given problem:

Q: If a = (1, 2, 1) and b cross products. 1. a × b : = 2. b xa = = (12, 15, 1), find the following

A:

Q: 16.) If u= (2, k, 1, 4) and v= (3,-1, 6,-3), find k such that ||u – v|| = 6

A: Given:        u=2,k,1,4         v=3,-1,6,-3     u-v=6      u-v=2,k,1,4-3,-1,6,-3…

Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

Q: Let A = -18 -15] 17 20 Find S, D, and S1 such that A = SDS-1 1 1 S- - BA] - PGI-1 D= = 1 2 0 -3

A:

Q: 8. Determine the dot product of u = [7,-4.1] and v = [3.-2.2].

A: Dot product is also known as the scalar product.

Q: Given i [2, – 5Jand i = [-7,2] find %3D b. ủ •

A:

Q: All of the following are equidistant from the point (6,8) EXCEPT о (6, —2) 0 (-2, 12) о (16,8) O…

A:

Q: Let S = {1,2,3,4, 5}, G = {(1),(123), (132)}. For each element %3D a e S, find stabc(a) and orbg(a)

A:

Q: At which of these times (A, B, C, D, E) was runner 1 stopped and runner 2 running? (Select all that…

A: From the graph it can be observed that, At time A the runner 1 had stopped and runner 2 was running,…

Q: 5. Evaluate J2xdx, a, x' +c b, x+c C. 2x+c

A:

Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find a. D' b. D-A c. P(A)

A: Note:-Since you asked multiple subparts,according to our policy we can solve only first three sub…

Q: If x-Gamm(a,B) and if a =1, then Gamm(1.B)-

A:

Q: Let X ∼ N ( 1 , 4 ) and Y ∼ N ( 2 , 9 )be independent and let W = X2 +2Y + 3. Then what is the mean…

A: Given, Therefore,

Q: Suppose E = {a, b, c, d, e, f, g, h, i, j}, %3D A= {a, b, c, d, e, f, g}, B= {b, d, f, i, j}, C =…

A: Given sets are

Q: a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} a1.…

A:

Q: In ADAT, mZD = 8x – 6, mLA 5z + 12, and m/T = 7x – 26. Find z and mZT. (Hint - Draw a picture…

A:

Q: If 1 A = -9 6 1 6. 2 -T and Q(#) = ' Až, then Q(z1, 12, T3) = Enter z1 as x1, 12 as x2, and 13 as…

A:

Q: Given v→ = and u→ = , find v→ + u→. v→ + u→ =

A: Given:     v  = ⟨ 10 , 2 ⟩      u = ⟨ -5 , 8 ⟩     v + u = ?

Q: If A%3 2x3 -Зх +2:х € [О, 2) then in (R, T,), A %3D а. [-3, 1] b. [-1, 1] с. [1, 3] С. d. [0, 4] e.…

A: Open sets and Closed sets: The sets in topology τ are called the open sets of the topological space…

Q: A = 2 1 2 0 1 -H B = W = w-B Find the following: a- A², AB, det(A) b- If AW=B, find (W) using…

A:

Q: ..***a***** . Let x (m, 1,0,-2)", m > 0 and ||x||2 = V30, then Select one: a. 6 b. 7 с. 5 d. 4

A:

Q: Let X B(25,0.2). E(X²) = Select one: O a. 41 Оъ. 29 О с. 25 O d. 0

A:

Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

A: Complex number and it's modulus

Q: dx, dt d²x₂ dx₁ + dt² dt 7. X₂ = a₁ 8. X3 = X₁

A:

Q: Let u = (6,6) and v = (5,6). Express 4u+7v in the form (a,b). 4u + 7v= ( (Simplify your answers.)

A:

Q: 13. Find the intersection of [x., y.=]= [4,-2.3]+ r[1,–1,7] and| [x, y, =]=[2.-4,11]+ s[3.1,–1].

A:

Q: If u x = [1, -3,5], thenx =

A:

Q: Let X=(1,0, – 1,-V2)'. Then, ||X||2 = Select one: а. 3 O b. 4 C. 2 O d. 1

A:

Q: Suppose x, y, z E R. Show that zz = yz if and only if either x=y or z = 0.

A:

Q: 8. If W = and V =, compute W x V.

A: To compute w*V from the given vectors.

Q: Q9. Let keep A = (a, b, c, 1, 2, 3). Let's Insert the appropriate symbol e or ¢ in the blank space.…

A: Concept: The letter Epsilon '∈' is used for the words 'belongs to', 'is an element of', etc.…