To solve: the system of linear equations
Answer to Problem 53E
The solution to the above system is equal to
Explanation of Solution
Given:
Consider the system of equations
Calculation:
Consider the following system of equations:
First translate the system of equations above into an augmented matrix as shown below:
Next use elementary row operations to convert the matrix into row echelon form.
To do this, start with the following row operation:
The fourth row corresponds to the equation
This equation is always true, no matter what values are used for x, y, z and w. Since the equation adds no new information about the variables, drop it from the system.
So the last matrix corresponds to the system is
Since z is not a leading variable
Therefore, it has infinitely many solutions.
Thus, the system is dependent.
Because
Because set
Next solve for y as shown below:
Next solve for x as shown below:
Therefore, the solution to the above system is equal to
Conclusion:
Therefore, the solution to the above system is equal to
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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