2. Given the system below,3x₁x₂2x3= 7x₁ + 7x₂-3x3 = -19x₁2x₂ + 10x3 = 71Use the Crout's / Cholesky Method to obtain the solution of the same system. Terminate ifEa ≤ 0.0001

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Answered: 2. Given the system below, 3x₁x22x3 = 7…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Solve the given system using LU- Factorization x₁ + x₂ + x3 = 3 x₁x₂ + 4x3 = 4 2x₁ - 2x₂ + 8x3 = 0
Q3. Solve the following linear system by Gauss elimination. Show the intermediate steps. 6x2 + 13x3 = 137.86 6x1 8xз — 85.88 13х1 — 8x. = 178.54
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1. How many solutions does the following 3 × 3 system have? x₁ + 2x₂ + x3 = 8 2x1 + 2x2 + 2x3 = 4 3x₁ + x2 + x3 = 6.
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7. Without graphing, determine how many solutions each system has. a. { 111 = X y = 2x b. 3x + 4y = 12 (2x + 4y = 8 no sol. C. PEK 1 y = = x + +1 =- √x+8 d. √y = -√√x + 2 -2y=-x-4 Which equations have the same slope? The system with one solution, no solution, or many solutions? C. Which equations have the same y-int? The system with one solution, no solution, or many solutions? d. Why is it sometimes hard to see that two equations are equilvalent?
2.x1 – 3x2 + x3 = 0 - Find the value of k for which the system of equations 1+ 2x2 – 3x3 = 0 has non trivial - 4.x1 – x2 + kx3 = 0 solutions.
4) Determine whether the given set of functions is linearly independent on the interval (-x,). a) (z) = cos 2z, (2) = 1, 1,()= cos z b) (z)=z, 1,(2)=z-1, (z)=z+3 c) ()=e**, 1,(=)=e
4.2) Solve the given system of equations using Gauss-Jordan Reduction method.
4. . Solve the linear equation systems 2x, +5x₂ + 2x, = -8 by using Crout method, where (x₁+2x₂ + 3x₂ = -3 fed arti hai (25) 3x₁ + x₂ + 5x₂ = 1 [1 2 3 -4 U = 0 1 001

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2. Given the system below, 3x₁x22x3 = 7 x₁ + 7x₂-3x3 = -19 x₁2x₂ + 10x3 = 71 Use the Crout's / Cholesky Method to obtain the solution of the same system. Terminate if Ea ≤ 0.0001