To describe: operation on a linear system that result in an equivalent system.
Answer to Problem 3RCC
1. Add a nonzero multiple of one equation to another.
2. Multiply an equation by a nonzero constant.
3. Interchange the positions of two equations.
Explanation of Solution
1. Add a nonzero multiple of one equation to another.
For example, if the system
Eliminate the X-term from Equation 1 by subtracting Equation 2 from Equation 1.
Our new system, with the new Equation 1, is
This is equivalent to the original system. Alternatively, add twice Equation 2 to Equation 1 in order to cancel the y-terms.
Our new system, with the new Equation 1, is
This is equivalent to the original system.
2. Multiply an equation by a nonzero constant.
For example, if the system
Multiply the second equation by 2 in order to get a -2y term.
This is equivalent to the original system.
3. Interchange the positions of two equations.
For example, if the system
Switch any two equations.
This is an equivalent system. This operation can also be used to identify triangular systems. The system
can be rewritten as
Now, use back-substitution more easily.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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