In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x , y ; or x , y , z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 1 0 0 2 | 1 2 3 ]
In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x , y ; or x , y , z ; or x 1 , x 2 , x 3 , x 4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [ 1 0 0 0 1 0 0 0 1 0 0 2 | 1 2 3 ]
Solution Summary: The author explains that the system of equations corresponding to the reduced row echelon augmented matrix has infinitely many solutions.
In Problems 27-38, the reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use
; or
; or
as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
Expert Solution & Answer
To determine
To find: The system of equations corresponding to the given reduced row echelon augmented matrix and find the solution, if possible:
Answer to Problem 34AYU
Solution:
Consistent system of equations, infinitely many solutions.
Explanation of Solution
Given:
Calculation:
The system of equations corresponding to the given reduced row echelon augmented matrix is:
Here we find that the number of equations is 3, whereas the number of variables is 4.
The number of equations is less than the number of variables.
So the above system of equations has infinitely many solutions.
University Calculus: Early Transcendentals (4th Edition)
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