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!
Chapter7: Matrices And Determinants
Section: Chapter Questions
Problem 15T: One hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a...
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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).
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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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