The system of linear equation is inconsistent or dependent. If the system is dependent to find the complete solution.
Answer to Problem 32E
The given system of equation has infinitely many solutions.
Explanation of Solution
Given:
Equation given,
Concept Used:
The concept to find the complete solution of the system using the row operations is used.
Calculation:
Consider first the given equations,
Step1:
In the first step first convert the given, equation into augmented matrix.
Now reduce the augmented matrix to convert it into row echelon form,
Step 2:
In the second step reduce the augmented matrix to convert it into row echelon form,
Transform the augmented matrix into row echelon form.
For this row operation is performed. In the first row operation,
Thus the matrix is now obtained in row echelon form,
Step3:
In the step 3write the echelon form of the matrix in equation form,
To get the values of
The equation can be written as,
As the variable
Conclusion:
Hence, the given system of equation has infinitely many solutions.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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