Can you please explain to me how does the answer in red square, come about? Please write in handwritten notes so i can see ths solution? Kindly please include general rules/formula that I need to consider if there's any, thankyou!
Can you please explain to me how does the answer in red square, come about? Please write in handwritten notes so i can see ths solution? Kindly please include general rules/formula that I need to consider if there's any, thankyou!
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Can you please explain to me how does the answer in red square, come about? Please write in handwritten notes so i can see ths solution?
Kindly please include general rules/formula that I need to consider if there's any, thankyou!
![EXAMPLE 9
SOLUTION
Solving a Homogeneous System of Linear Equations
Solve the system of linear equations.
x₁ - x₂ + 3x₂ = 0
2x₁ + x₂ + 3x3 = 0
Applying Gauss-Jordan elimination to the augmented matrix
01
3
1 3
yields the matrix shown below.
1-1 3
:]
3 -3
-1
C
-1 3
-1
:]
01
R₂ + (-2)R₁ →R₂
+ 2x3 = 0
X₂ X3 = 0.
GR₂ R₂
R₁ + R₂ R₁
0 2
[
1 -1
The system of equations corresponding to this matrix is
X₁
Using the parameter 1 = x3, the solution set is
x₁ = -21, x₂ = 1₁
x3 = 1,t is any real number.
This system of equations has an infinite number of solutions, one of which is the trivial
solution (given by t = 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb39ec2d0-e884-4a3b-8462-fc37a0c6c2b4%2Fcbd16555-b1ba-424b-a8a1-51bd3b7ed4b5%2Fyub22l5_processed.png&w=3840&q=75)
Transcribed Image Text:EXAMPLE 9
SOLUTION
Solving a Homogeneous System of Linear Equations
Solve the system of linear equations.
x₁ - x₂ + 3x₂ = 0
2x₁ + x₂ + 3x3 = 0
Applying Gauss-Jordan elimination to the augmented matrix
01
3
1 3
yields the matrix shown below.
1-1 3
:]
3 -3
-1
C
-1 3
-1
:]
01
R₂ + (-2)R₁ →R₂
+ 2x3 = 0
X₂ X3 = 0.
GR₂ R₂
R₁ + R₂ R₁
0 2
[
1 -1
The system of equations corresponding to this matrix is
X₁
Using the parameter 1 = x3, the solution set is
x₁ = -21, x₂ = 1₁
x3 = 1,t is any real number.
This system of equations has an infinite number of solutions, one of which is the trivial
solution (given by t = 0).
Expert Solution
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Follow-up Questions
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Follow-up Question
why is the x3 was chosen as the free variable? is that always gonna be the case?
Solution
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