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 0 1 0 0 0 0 1 0 0 0 0 1 | 1 2 3 0 ]
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 0 1 0 0 0 0 1 0 0 0 0 1 | 1 2 3 0 ]
Solution Summary: The author explains that the system of equations corresponding to the reduced row echelon augmented matrix is consistent or has unique solution.
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 36AYU
Solution:
Consistent system.
Explanation of Solution
Given:
Calculation:
We find that the rank of the coefficient matrix is 4.
The rank of augmented matrix is also 4.
Both the ranks are equal and is equal to 4.
Moreover the number of variables and the number of equations are also 4.
Hence the system of equations is consistent or has unique solution: .
Thomas' Calculus: Early Transcendentals (14th Edition)
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