Consider the following system of linear equations, 3x3 + X4 -1 2x3 + 2x4 = 7 5x3 + 3x4 = 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: 2x1 + X1 3x1 -2x1 X2 + 2x₂ + 3x₂ - - - 1- Write the system in matrix form (Ax = b) 2- Write the augmented matrix 11
Consider the following system of linear equations, 3x3 + X4 -1 2x3 + 2x4 = 7 5x3 + 3x4 = 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: 2x1 + X1 3x1 -2x1 X2 + 2x₂ + 3x₂ - - - 1- Write the system in matrix form (Ax = b) 2- Write the augmented matrix 11
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7a7cf5d-31a2-4576-8cd3-b9249db64bed%2F7aefdb75-f2d7-4eee-98d6-c7dc9b32e194%2Fia8x7j_processed.jpeg&w=3840&q=75)
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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