Complete solution of linear system or show that it is inconsistent.
Answer to Problem 21E
The solution for the linear equations in three variables is
Explanation of Solution
Given:
Equation’s given in three variables are,
Concept Used:
There are two step in solving the linear system :
In the first step convert the triangular system into the Gaussian elimination.
In the second step use the back substitution to find the values of all variables.
Calculation:
Consider the given equations in three variables
First step:
Interchanging the first and second equation,
Now in the first step first to convert the given equation Gaussian elimination is used. In the final step the triangular system will be in which the first equation will contain all the three variables, second will contain two variables and the third equation will only contain one variable.
Consider the second equation and replace it by adding
The new equation obtained will be,
Now to eliminate
The new equation obtained will be,
To eliminate y , add a negative from the new equation obtained.
Thus the triangular system becomes,
Third Step:
Now in the last step find the values of
Consider equation
Substitute the value of
Now put the values of
Conclusion:
Hence, the solution for the linear equations in three variables is
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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