9. Consider the following system of linear equations,x₁ + 2x₂ + 2x3 + 3x4 = 42x1 + 4x₂ + x3 + 3x4 = 53x₁ +6x2 + x3 + CX4 = 7where c is a constant. For what values of c does the above system(a) has no solutions?(b) has a unique solution?(c) has infinitely many solutions? Find the solution set.

We have to find the value of c for which given system of linear equations has no solution, has a…

Answered: 9. Consider the following system of…

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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(1 point) (Note: This problem has several parts. The latter parts will not appear until after the earlier parts are completed correctly.) Part 1 Solve the following system of linear equations: + 5y 5z 25 2x 11y 11z 55 - 3x 16y 16z 80 - 9y 9z 45 Which one of the following statements best describes your solution: A. There is no solution. B. There is a unique solution. C. There are 3 solutions. D. There are infinitely many solutions with one arbitrary parameter. E. There are infinitely many solutions with two arbitrary parameters. F. There are infinitely many solutions with three arbitrary parameters. Statement: Part 2 Enter your solution below. If a variable is an arbitrary parameter in your solution, then set it equal to itself, e.g., w = w. X = y = Z = ... 出|田 +
X1 = x2 = || || x3 Solve the following system of three linear equations in three unknowns. 2x₁ +6x₂ + x3 = -2 x₁ + 3x₂ = -2 4x₁ +8x₂ + x3 = -2
1. Solve the system of linear equations 3x + 2y 2 6x + 4y b 2-2 +4² y-1 3 C X- X1 - 3y 2x2 3x1 + 2x2 - - TE 14 2 20 + 5x3 = X3 2
b) Solve the above system of linear equations using LU-decomposition.
6. Solve the system of linear equations 2x₁ + 2x₂ + 4x3 16 4x₁ + 2x₂x3 = 6 -3x₁ + x₂ − 2x₂ = 0 a. by Gauss-Jordan elimination. b. by inverse method.
1. Solve the following quadratic systems: y = x2- 5x + 7 and y = 2x + 1 y = 2x2- x - 2 and y = x2-5x-6 y-x2=7-5x and 4y-8x=-21
Q3. Solve the following system of linear equations by a direct method: 4x - 3y + 5z = 34 2x-y-z = 6 3x + y - 4z = -1

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9. Consider the following system of linear equations, x1 + 2x2+2x3 + 3x4 = 4 2x1 + 4x2 + x3 + 3x4 3x1 + 6x2 + x3 + x4 = 7 where c is a constant. For what values of c does the above system (a) has no solutions? (b) has a unique solution? (c) has infinitely many solutions? Find the solution set.