D3, S ymmeteies of an Equillateral triang le 4123) (34 (23) (13) 42) )= Po fo M2 M3 M. C123)=p P My Po (23) = My MI Po C13) = 42 (12) = Mg My fo Find the cube of each element in S3 = D3, i.e. for each x ED 3, find %3D the element x in D3. P.

Q: QUESTION 8 List the elements in (3))in Z 18 -

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Q: How do you calculate ophat? 0% b/f P(1-P) 12 OP(1-P) √n Ophat-(1-phat) √n phat-(1-phat) TL

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Q: (h) T 2. Find each of the following: (a) l쉬 (b)IT|

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Q: 2-201 0 1 1 1 103 A = 0 1 -1 3 0 1 1 1 1 1 1 Which is the element A3,2?

A: To find the element A3,2  of the given matrix A.

Q: why is algebra important? What are some interesting things about algebra? What are some pros and…

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Q: Find all elements of order 5 in Z15.

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Q: For circuit M, find out what orders its nonzero ones have elements and find their divisors of zero,…

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Q: 4 The factorization of 12x + 15 is

A: firstly we write function as multiple of its number and then we take out common outside.

Q: QUESTION 2 1 2 3 4 5 6 7 8 1 2 3 4 5 678 = 3 8 4 1 6 7 25 %3D T = 6 4 1 2 7 853 1. Write each of the…

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Q: Kailashben

A: The objective of this question is to find another permuted LU factorization of the given matrix A.…

Q: QUESTION 12 Given a = (1 3 5 6 7)(2 3 5 6 7) in Sg. a) (3) Write a as a cycie or a product of…

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Q: Find the value of 1 1 1 (1+ a) 1 1 18- ( 1² + ²b) |

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Q: Find ATI A21, IAATI, 12A1, and A-¹1. 5 0 3 A 6-1 4 L2 5 11 51

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Q: True

A: False.

Q: Find the order of each element in Z12-

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Q: 4 1 [1 -1 2] [2 3] +|0 1

A: Given matrix expression: 1-12 4-10 23 + 1001-1-1

Q: a12 ain a21 a22 a2n C2 and c = then express the product Question 2(a): If A = Cn Am2

A: The given matrices A and C are: As in matrix A has "m" rows and "n" columns and in matrix C has "n"…

Q: Find the order of (3, 4) in Z4 × Z6

A: Z4={ 0,1,2,3 } mod 4Z6={ 0,1,2,3,4,5 } mod 6Order (a,b) in Zm*Zn = LCM { order( a), order (b)}

Q: Ms. Kemp asks her students throughout the year to record the number of hours per week they spend…

A: Best fit line can be identified by 2 methods first is  eye ball method which states that draw a…

Q: 4. Perform the indicated operations. -2 1] a) [1 -4] 0 1 5 1 b)| 0 4 13 4

A: We have to perform

Q: 3. (a) Write o as a product of transpositions.Is this permutation even or odd? (b)Write t as a…

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Q: EXAMPLE 3 Division 1+ 3i 1+ 3i 3 – 2i = 3+ 2i 3+ 2i 3 – 2i 1(3 – 2i) + 3i(3 – 2i) 3(3 – 2i) + 2i(3 –…

A: We have to simplify 1+3i3+2i Rationalizing the denominator,…

Q: Question 2 Expand (4+x)5 giving your answer in its simplest form.

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Q: How do you write the quotient in the simplest form? 3x 6x2 2x-4 x-2 3x

A: We have to find the answer in simplest form .

Q: Prove that n2+ 4n + 6 E O(n²)

A: Solution: The objective is to prove that the given statement

Q: 2. Which of the following is equivalent to (2x)° ?

A: Given that, 2x36 here we use power rule to expand the given iteration.

Q: Ep1(90 + 1) (iii) Epo(9o + 91) Χ 100 Ep1 V9091 (iv) Epo vg091 Χ 100

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Q: 4. 5. Find det(4A). Find the adjoint of A.

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Q: Abstract

A: We find cosets in U(15).

Q: Show that if a ú an odd integer, thn a =1 (md 16).

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Q: Find the order of each element in U(15).

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Q: QUESTION 13 List all the elements of order 12 in Z600.

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Q: Find the inverse of each element in U(7).

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Q: Let p be a prime and n a positive integer. Prove that if o(pn) = po(n) then pin.

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Q: 3. 2 -3 The matrix product 4 1 1

A: Follow the next step for explanation.

Q: QUESTION 11 13 Let A then A-1 %3D

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Q: Can you find LU factorization of A, thank you.

A: The obtained matrices are

Q: Show that if ac | bc, then a | b. (Assume that c is not zero.)

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Q: QUESTION 5 Find all the elements of order 12 in Z48000 -

A: Number of elements of [m] in Zn is phi(m)

Q: The columns of 13 = 0 1 0 X₁ OA. TX₂ X3 X₁ for the image of an arbitrary x= x₂ in R³. (င်)- X3 X₁…

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