Consider the following system of linear equations, 3x3 + 2x1 + X2 X1 + 2x₂ + 3x₂ 3x1 -2x1 -1 7 6 X2 5x3+4x4 = -3 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: - X4 2x3 + 2x4 = 5x3 + 3x4 = 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- Eliminate the zero rows 5- number of free variables = number of variables - number of nonzero rows 6- replace the free variables with parameters (distinct parameters) 7- find the remaining variables in terms of the parameters)
Consider the following system of linear equations, 3x3 + 2x1 + X2 X1 + 2x₂ + 3x₂ 3x1 -2x1 -1 7 6 X2 5x3+4x4 = -3 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: - X4 2x3 + 2x4 = 5x3 + 3x4 = 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- Eliminate the zero rows 5- number of free variables = number of variables - number of nonzero rows 6- replace the free variables with parameters (distinct parameters) 7- find the remaining variables in terms of the parameters)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 4CEXP
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Transcribed Image Text:Consider the following system of linear equations,
3x3 +
2x1 + X2
X1 + 2x₂
+3x₂
3x1
-2x1
-1
X4
2x3 + 2x4 =
5x3 + 3x4 =
7
6
X2
5x3+4x4 = -3
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:
-
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- Eliminate the zero rows
5- number of free variables = number of variables - number of nonzero rows
6- replace the free variables with parameters (distinct parameters)
7- find the remaining variables in terms of the parameters)
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