Find all solutions to the equation [50]114 Y = [8]114 for Y EZ114. Justify your answer.
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Can yuo please help with, part b, thank you.
![3 (a) Using Euclid's algorithm, solve the equation [25]57 X = [4]57 for X € Z57.
Show your working.
(b) Find all solutions to the equation [50]114 Y = [8]114 for Y Z114. Justify your
answer.
[Hint: for part (b) you should notice that ([50]114)-1 doesn't exist. Instead, write
out what the equation means in terms of ordinary integers, and then relate it to part (a).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4082be17-8615-459e-878a-685f4f1bd2cd%2Ffca16a5a-17d2-4921-812d-c7551aeaac05%2Fb2o7m0d_processed.jpeg&w=3840&q=75)
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- Consider the following LP:min 5x1 + 4x2s.t. x1 + x2 ≥ 12x1 − x2 ≥ 13x2 ≤ 2x1, x2 ≥ 0.a. Write down the dual of this LP.b. We know that by strong duality, we can either solve this LP or its dual form to get the sameoptimal objective value. If you apply the simplex algorithm, which one would you rathersolve? Make your choice and apply the simplex algorithm to solve it.Consider the following LP:min 5x1 + 4x2s.t. x1 + x2 ≥ 12x1 − x2 ≥ 13x2 ≤ 2x1, x2 ≥ 0.1. Write down the dual of this LP.2. We know that by strong duality, we can either solve this LP or its dual form to get the sameoptimal objective value. If you apply the simplex algorithm, which one would you rathersolve? Make your choice and apply the simplex algorithm to solve it.Derive the fourth order Runge Kutta method in which k¹,k², k³ and k⁴ are to be find in detail steps.
- How exactly does one go about utilizing numerical methods to solve a set of equations that have been arranged in a system? Provide your own explanation of the algorithm used in at least one of the methods.Use the Newton-Raphson Method to find an iterative algorithm for finding the solution of the equation arctan x = x2− 3Solve for x, y and z using the Elimination Algorithm. And conclude appropriately what kind of values do the x, y and z represent.2x + 2y + 2z = 42x – 2y + 2z = 84x + 4y + 2z = 6
- I need a complete solution for 2 problems mentioned in the pictures below, these are from the Numerical-Analysis subject. In case it has to be solved through programming (eg Matlab), just provide me the correct theory & algorithm that can be used for the corresponding excercise. Thank you.We want to find the number of ways in which 3r balls can be selected from 2r red ballsand 2r blue balls. Find the generating function corresponding to the above problem in closed form.Show that the diophantine equation x^4 - y^4 = z^2 has no solutions in nonzero integers using the method of infinite descent
- First 3 parts are solved. 5-28 Consider the linear programmax x1 + x2s.t. x1 + x2 ≤ 9-2x1 + x2 ≤ 0x1 - 2x2 ≤ 0x1, x2 ≥ 0(a) Solve the problem graphically.(b) Add slacks x3,c, x5 to place the modelin standard form.(c) Apply rudimentary simplex Algorithm 5Ato compute an optimal solution to yourstandard form starting with all slacks basic.(d) Plot your progress in part (c) on thegraph of part (a).(e) How can the algorithm be making progress when l = 0 if some moves of part(c) left the solution unchanged? Explain.5-29 Do Exercise 5-28 for the LPmax x1s.t. 6x1 + 3x2 ≤ 1812x1 - 3x2 ≤ 0x1, x2 ≥ 0How do you solve the addition problem using lattice algorithm?How to solve this problem with the dual simplex algorithm: max 60x1 + 30x2 + 20x3subject to8x1 + 6x2 + x3 <= 484x1 + 2x2 + 1.5x3 <= 202x1 + 1.5x2 + 0.5x3 <= 8x1 + x2 + x3 <= 11 x1,x2,x3 >= 0