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Consider the following system of linear equations, 2x₁ + 3x3 + = -1 = 7 X1 3x₁ + 3x₂ 5x3 + 3x4 = 6 4x1 + 5x₂ 7x3 + 5x4 = 10 Use Gauss Elimination method to show that the above system has infinite number solutions (there are free variables) and hence find that solution in parametric form (Hint: X2 + 2x₂ - - X4 2x3 + 2x4

Consider the following system of linear equations, 2x₁ + 3x3 + = -1 = 7 X1 3x₁ + 3x₂ 5x3 + 3x4 = 6 4x1 + 5x₂ 7x3 + 5x4 = 10 Use Gauss Elimination method to show that the above system has infinite number solutions (there are free variables) and hence find that solution in parametric form (Hint: X2 + 2x₂ - - X4 2x3 + 2x4

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 72E: Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by...
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Consider the following system of linear equations, 2x₁ + 3x3 + X4 2x3 + X2 -1 7 X1 3x₁ + + 2x₂ 3x₂ 5x3 + 3x4 = 6 4x₁ + 5x₂ 7x3 + 5x4 = 10 Use Gauss Elimination method to show that the above system has infinite number of solutions (there are free variables) and hence find that solution in parametric form. (Hint: 2x4 = 1- Write the system in matrix form (Ax = b) 2- Write the augmented matrix 3- Use row operations to transform the augmented matrix into the Echelon form 4- Notice the contradiction)
Transcribed Image Text:Consider the following system of linear equations, 2x₁ + 3x3 + X4 2x3 + X2 -1 7 X1 3x₁ + + 2x₂ 3x₂ 5x3 + 3x4 = 6 4x₁ + 5x₂ 7x3 + 5x4 = 10 Use Gauss Elimination method to show that the above system has infinite number of solutions (there are free variables) and hence find that solution in parametric form. (Hint: 2x4 = 1- Write the system in matrix form (Ax = b) 2- Write the augmented matrix 3- Use row operations to transform the augmented matrix into the Echelon form 4- Notice the contradiction)
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