The solution of given system of linear equations having unique solutions using Gaussian elimination or gauss-Jordan elimination.
Answer to Problem 26E
The solution for given system is
Explanation of Solution
Given:
Equation given,
Concept Used:
The concept of Gaussian elimination is used to concert the linear system into row echelon form.
Calculation:
Consider first the given equations,
Step1:
In the first step first convert the given, equation into augmented matrix.
Step 2:
In the second step elementary row operations are performed to transform the augmented matrix into row echelon form.
For this row operation is performed. In the first row operation,
Again the next row operation is,
Step3:
In the Step3 again perform the row operations as follows,
The next operation to be performed is,
Again the next elementary row operation is,
Step 4:
This step is called row-echelon form,
In the step 4 divide the
Now the matrix is obtained in the row echelon form , write the equations from the matrix,
Step 5:
The value of
From equation
Substitute the value of
To find
Conclusion:
Hence, the solution for given system is
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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