To solve: the system of linear equations
Answer to Problem 52E
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:
Because there is no fourth row, conclude that there are infinitely many solutions to the system above.
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 w is not a leading variable
Therefore, it has infinitely many solutions.
Thus, the system is dependent.
To obtain the complete solution, solve for the leading variables x, y, and z in terms of the non-leading variables w, and let w be any real number.
Therefore, set
Next solve for y as shown below:
Next solve for x as shown below:
Conclusion:
Therefore, the solution to the above system is equal to
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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