Whether the augmented matrixof the given system of linear equation is row equivalent to its row-reduced echelon form.
Answer to Problem 6E
The augmented matrix of the given system of linear equation is row equivalent to its row-reduced echelon form.
Explanation of Solution
Given information:
A system of linear equation is given as
Concept used:
Co-efficient matrix of a system of linear equation of the form
The augmented matrix of the system of linear equation is given by
A matrix is in row echelon form if it has the following properties:
- Any rows consisting entirely of zeros at the bottom of the matrix.
- For each row that does not consist entirely of zeros, the first nonzero entry is 1.
- For two successive rows, the leading 1 in the higher row is further to the left than the leading 1 in the lower row.
And a matrix in row-echelon form is in reduced row echelon form if every column that has a leading 1 has zeros in every position above and below its leading 1.
Consider the given system of equation.
Now, the augmented matrix is given by
Now, perform row operations as shown:
Apply
Apply
Apply
The above is the reduced row-echelon form of the given matrix.
Therefore, the augmented matrix is row equivalent to its row-reduced echelon form.
Chapter 7 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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