In the diagram below, prove that AKLM = AKNM. K

Q: Find all values of z for which z* + 2 – i2v3 = 0 and represent them geometrically.

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Q: Let A [ - 5 13 12 13 2333 12 13 5 Explain why A-₁ = AT. -1 13

A: Step 1:

Q: Which numbers satisfy lal = a? Which satisfy lal = -a? What about I-al= a?

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Q: Let n 2 2. Assume that Fn is prime. show that Fn = -1.

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Q: Assuming that gcd(a , b) = 1, prove the following: (b) gcd(2a +b, a +2b) = 1 or 3.

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Q: Q. 5 Given that A and B are independent with P(AUB) = 0.8 and P(B)= 0.3, find P(A).

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Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

Q: Find the class equation of G= {I, a, a², ß,ßa,ßa²|a² = ß² = (aß)² = I }

A: Here first identify the number of element of the group and group itself: given that α2=β2=αβ2=1The…

Q: Let G = S4 and H = D4. Write down the distinct right cosets

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Q: (2) For each nEN, set D= [ Find each of the following (2) U Dn. (b)

A: Given Dn = -7n, 5n

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: To show that the group <a, b | a^5 = b^2 = e, ba = a^2b> is isomorphic to Z2, we need to…

Q: A. j2n = (-1)" B. jan+1 = j C. j¯" = (-j)" D. jan-1 = –1

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Q: Find all the values of In(4 – 4j). What is its principal value?

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Q: Let H = {(1), (12)(34), (13)(24), (14)(23)}. Find the left cosets of H in A4 (see Table 5.1 on page…

A: Given H = (1), (12)(34), (13)(24), (14)(23) in A4 H =4and A4 =4!2 =12 So , Number of distinct left…

Q: Let 1)" Find sup A and inf A. Provide some explanations how you got their values or why they don't…

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Q: verify that (AT )T = A

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Q: tan(z1) 0.9947 + 0.1462i 0.0364 1.0047i

A: The definition of tangent function for complex number is tanz=e2iz-1i(e2iz+1). Use 4-2i for z1 and…

Q: Show that A × B ≠ B × A, when A and B are nonempty, unless A = B

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Q: Establish the identity arg() = argz1 – argz2 .

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

Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: Find ſ using residues.

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Q: (1-exjdy of 28 on Find the halutiom

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Q: Let a = . Find Ja]. - 2, 2,1 >. Find lä].

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Q: Show that if we make the change of variables =x – ct and n =x + ct, then, as in (16.7), a?u ,a²u a…

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Q: Let á = . Find Jä].

A: Let's learn the concept.

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: We have to show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

Q: a = 268 b = 752 e. Prove that if g = gcd(a, b) then gcd (2) = = 1

A: Given that a = 268 = 2 × 2 × 67 b = 752 = 2 × 2 × 2 × 2 × 47   Now let g = gcd (a, b) = gcd ( 268,…

Q: 1. Let A = 111, F(t) = %3D %3D 1 0. Find the solution of the initial value problem: X' = AX + F(t),…

A: 1. The given informations are,A=111111111, F(t)=111 and η=000

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: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given: m divides nWe need to show that GFpn:GFpm=nm

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given : m divides n . To prove : GFpn:GFpm=nm.

Q: find​ Pr[A ∩​ B].

A: Given : Pr[A ∪​ B] = 0.76 ​, ​Pr[A] = 0.36 ​, Pr[B] = 0.46 ​ Our aim is to find​ Pr[A ∩​ B] Here ,…