Let c, a, B be nonzero real numbers such that c + B. Find a given that 72n-3 Σ19 ac? cn-4 c - B' n=3 O 6510 6468 6566 6524 6174 6517

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 92n 3 6. cn 4 ac? Türkçe: c,…

A: To find the value of a from the given summation.

Q: 4. Let IR be the set of all real numbers, xER and n EN such that n 2 2. If (1+x)> 0, prove that Pn :…

A: Let ℝ be the set of all real numbers,  Let x∈ℝ and n∈ℕ such that n≥2 where ℕ is the set of natural…

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

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Q: 3. Let H≤ G. Then the number of left cosets of H in G is [G:H]. *True *False

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Q: ii. Show that the image of the hyp n2 = cos2n

A: Introduction: Inversion and Reflection: The transformation is w=1z.

Q: Q1. Prove that for any natural number n, E, 2i = 2n+1 – 1. i%3D0

A: I have used mathematical induction to prove the result

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 192n 3 18 cn 00 ac? 4 C - n-3…

A: To find a from the given summation

Q: 3. Find two elements a and b in Z25 such that a and b are units, but a +b is not a unit. Justify…

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Q: . Consider a = 7+ 2i andB = 3 – 4i in Z[i]. Find o and p in Z[i] such that ine = βσ+ ρ with N(p) <…

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Q: Determine all s ∈ R such that I4s= (I4)s

A: Given I4s=(I4)s We know I4=1 I4s=(1)s

Q: 5. In the figure below, AD and AE trisect ZBAC. Prove that AC- AE - BD = AB- AD-EC. 2. DE

A: Angle bisector theorem:  In a triangle, the angle bisector divides the opposite side in the ratio of…

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: Prove that A=I-N+N²-N³ for A & N definec as follows: N=A-I (identity), where |1 0 0 an & I= 0 1 0. 0…

A: given matrix  A=1a12a1301a23001 and I=100010001 prove  that A-1=I-N+N2-N3 where N=A-I

Q: Q3- Give an example of two denes not equal X subsets of (R,T) and (z, of ). ( Explain your answer ).…

A: Answere : The two example are given below :

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

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Q: Let A & M and μ*(A) < oo. st B₁, B2,..., BEC, k <co with Bin B „²(AAŬB₂) <« j=1 any two sets E₁ and…

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Q: 3. Let G = Q3. Find the right cosets of H in G for: a) H = ( K). b) H = (-1).

A: Let G=Q8. We need to find the right cosets of &lt;K&gt; and &lt;-1&gt;.

Q: Let n be a positive integer. Let H = {0, ±n, ±2n, ±3n, . . .}. Findall left cosets of H in Z. How…

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Q: F. Find Ker() and o(25) for o: Z → Z, such that o(1) = 4. %3D

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Q: Let n >1. A hexagonal number h, is of the form h, = n(2n – 1). - a. Determine the first 5 hexagonal…

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Q: Deter mine The modulus t argument of @ 2+j4 O j(2-j) Ans/@4.472, 6326 2.236, 63 2i

A: (a) The given complex number is: z=2+j4|z|=(2)2+(4)2      =4+16      =20      ≈4.472And…

Q: Let A= 3 (n) Compute det (A) using a cofactor expansion along row 2. (b) Find A adj(A). (c) Find det…

A: Result: If determinant of matrix is a than determinant of  inverse of matrix is 1a. Transpose of…

Q: Find the conjugate and modulus of the following: (i) (1 + i³) – (4 + 3i) + (7 – 9i*) (ii) 7 +i° + (6…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: HewB Let - ! Frnd flA) Ans/ P)-(L-cosat) 4 Shなs

A: In this question we use Laplace transform property to solve this given function.       Here i…

Q: 4. Let R be the set of all real numbers, xER and n EN such that n 2 2. If (1+x) > 0, prove that Pn:…

A: Let ℝ be the set of real numbers, x∈ℝ and n∈ℕ such that n≥2. If 1+x&gt;0, we want to prove that  Pn…

Q: In the figure shown, CF intersects AD and EH at points B and F, respectively. G Complete the proof…

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Q: nex}. 2n (b) Let B = :nE 3n+1 i. Prove that inf B = ii. Show sup B =

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Q: b) Given that z, = V3 +i and z, = -2- 3i . Find the modulus and argument of and %3D Hence, express…

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Q: 2. Identify which of the following subsets ofR are closed, open, or neither. a. (zz is an integer}…

A: Answer

Q: 34. P(n): (cos 0 + i sin 0)" cos no + i sin nð

A: P(n): (cos θ+i sin θ)n=cos nθ+i sin nθ

Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: Let a = e =es and consider the set U₁8 = {1, a, a²,..., a¹7}. Give the elements of U18 (as powers of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Which of the following can you not use to prove A CAT S A DOG? 1. CA DO II. ZC ZD III. ZA E ZOo IV.…

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Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

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Q: Let Z3[i] = {a + bi : a, b ∈ Z3, i2 = −1} where arithmetic is done mod 3. 1.  Is Z3[i] an integral…

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Q: Prove that there exist c1, c2 ER such that for all ne N C1 E1 sin (i)<c2 =D1

A: We will use the range of the sine function to determine the real constants c1 and c2

Q: Find the value of k such that A is singular. 1 05 6 -1 0 4 5 k k. %3D

A: If the determinant of a matrix is zero then the matrix is singular.

Q: LLet G = Z/120Z and H = (48) < G. How many distinct cosets of H are there in G?

A: Given group G=ℤ/120ℤ subgroup H=48 The objective is to find the number of distinct cosets of H in G.

Q: The modulus of 5 + 4i is * O-41 O-√41 O√41 041 The conjugate of (i-i²)³ is O-2-21 2+2i -2+2i Oi-1

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Q: 3) Let II" , m i=1 where p1 0 integers. Show that d eN is a divisor of m if and only d = II p§ª…

A: Prove the theorem.

Q: Q7 Given that z = -1+3i. (i) Find z. (ii) Hence, plot the z in Argand diagram and find the modulus…

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Q: 3. Prove that A=I-N+N²_N³ for A & N defined as follows: N=A–I (identity), where 1 0 0 & I=|0 1 0 1…

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Q: Let z = cos + isin, and let a = z + 22 + z* and b = 2³ + 25 + 2®. Show that when a + b = -1 and ab =…

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Q: 5. All right cosets of H ≤ G have the same size. *True *False

A: 5. All right cosets of H≤G have the same size. True or False.

Q: Find the value of k such that A is singular. 1 0 5 5 -1 0 2 5 k k II

A: Given query is to find the value of k for which matrix A is singular.

Q: Find the value of k such that A is singular. 1 0 6 4 -1 0 6 2 k

A: Given. A is a 3X3 matrix. We need to find the value of k for which the matrix is singular. Singular…

Q: Find the value of k such that A is singular. 0 4 6 -1 0 4 2 k k =

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Q: (d) Prove that IJ CINJ. Give an example where 1JÇINJ. (e) Is (ab a e 1,beJ} an ideal in R?

A: ANSWER :

Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B