The system of linear equation is inconsistent or dependent. If the system is dependent find the complete solution.
Answer to Problem 34E
The given system has solution
Explanation of Solution
Given:
Equation given,
Concept Used:
The concept to find the complete solution of the system using the row operations is used.
Calculation:
Consider first the given equations,
Step
In the first step first convert the given, equation into augmented matrix.
Step
In the second step reduce the augmented matrix by using elementary row transformation to convert it into row echelon form,
Transform the augmented matrix into row echelon form.
The first row operation is,
Step
The next step of the row operation is,
Now the next operation to be performed to get the
Step
The next row operation to be performed is,
From the above matrix the third row has equation,
As the equation does not have any information it can be neglected from the matrix.
So, the remaining equations are,
As,
Thus the system is dependent.
Step
As the system has infinitely many solutions based on the above matrix in which
Substitute the value of
Conclusion:
Hence, the given system has solution
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning