The system of linear equation is inconsistent or dependent. If the system is dependent to find the complete solution.
Answer to Problem 31E
The given system of equation has infinitely many solutions and dependent.
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,
Step
In the first step first convert the given, equation into augmented matrix.
Step
In the second step by using elementary row operations transform the augmented matrix to convert it into row echelon form,
Transform the augmented matrix into row echelon form.
The first row operation is,
And,
The next operation to obtain is,
And,
Step
The next step of the row operation is,
From the above matrix the third row has equation,
As the equation does not have any information it can be neglected from the matrix.
So, the remaining equations are,
As,
Thus the system is dependent.
Conclusion:
Hence, the given system of equation has infinitely many solutions and dependent.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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