Determine the orders of the elements of D∞

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

A:

Q: (c) Give one example where the Green theorem fails, and explain how.

A:

Q: Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a…

A:

Q: a. Let X = {2, 4, 6} and Y = {a, b, c, d'}. Define g : X→ Y by the following arrow diagram. X 2 4 bo…

A:

Q: 1. Answer all parts. (a) Consider the operators A and B. Show that (i) (ii) [A, B]=-[A, B] [Am, A"]=…

A: Operators :A and B

Q: Let A = 1 -X -X X 1 -x X X -1 Find x such that A is invertible.

A:

Q: 1 2 Let A = 2 3 1 and C = 0 -2 1 1 | 1 B = -2 Find the trace 3 1 1 1 of (2AB + C)T.

A:

Q: Let T: M2x2 → P2 is a transformation defined as follows: b 7(₁2)=a+ = a + (b+c) x + (d + C Determine…

A: I have given the answer in the next step. Hope you understand that

Q: If z1 and zą both satisfy z +z = 2 |z - 1| and arg (21– 2): then find Im (21 + z2). 4'

A: let z1 = x1+iy , z2 = x2+iy2

Q: Use the adjoint of A = [1 [1 -5 -2 27to 1 to find A-¹ 0 2

A:

Q: Determine whether each of these functions from R to R is a bijection.  f(x)=2x+4

A:

Q: show that |z3|  ≠ |z4|  it is verified that |z1+z2/z3+z4|  ≤ |z1|+|z2|/|z3|-|z4|

A:

Q: Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b.…

A: This question related to function and bijection.

Q: Complete the table to express the values of each of these Boolean functions. F(x, y, z) xỹ + (xyz)…

A:

Q: If A has a row or column consisting entirely of zeros, then Select one: a. det(A) = 1. b. det(A) =…

A: Given a matrix A whose every entry is 0.

Q: Find the value of a for which U = a 1 10 is in the set 0 -1 3 0 H = span 5 3 -1 2 -2 -2 a =

A: The value of a=-7 .Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Determine whether the following set of polynomials is linearly independent (1 – t)?, t – 2t2 + t³,…

A:

Q: Let z E (-1,0) and let R, (z) be the remainder in Maclaurin's formula for In(1+z) in Cauchy's form.…

A: Given the function is fx=ln1+x

Q: 5d rd-2a 2b a D. 5e-h If det d Lg h i 1, compute det e If - 2c %3D C 5f-

A: To compute determinant of the given matrix.

Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

A:

Q: (b) Let A and Bị be independent; similarly, let A and B2 be independent. Show that in this case, A…

A:

Q: Set f(a,b) = (1+ a + b) + (2 + 2a + b)x + (1 + a + 26)r² and F = {f(a, b) : a,b e R} a subset of…

A: Given that fa,b=1+a+b+2+2a+bx+1+a+2bx2 and F=fa,b : a,b∈ℝ is a subset of ℝ2x. The objective is to…

Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

A:

Q: Which ones are echelon form, reduced echelon form or not echelon form?

A: To find which of the matrices are in echelon form, reduced echelon form or not in echelon form.

Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

A:

Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: Find 1 L L 0 0 (3x + 2y) dxdy

A:

Q: LetP(A) = 0.20, P(B) = 0.80, andP(A∩B) = 0.16. Are A and B independent? Justify your result…

A:

Q: In Exercise, verify that S and T are inverses.

A: Given, S and T are inverses if S∘T=T∘S=I

Q: D A B D Zax Zo Z₂ Z₂ x Z₂ ({0},+) E Z₁ Which one of the following is isomorphic to Z4 x Z6/((1,1))?

A:

Q: Consider the following three transformations from R³ to R³: x1 T x2 x1 - 2x3 2x1 - 2x2 - 5x3 x1 x1+5…

A: Step 1:Step 2: Step 3: Step 4: