584 Final Exam
(c) We can increase the value of c 1 , leaving everything else the same.
(d) We can decrease the value of c 2 , leaving everything else the same.
(e) We can reverse the sign of a 2 , leaving everything else the same.- Suppose someone claims that she has come up with a way to solve a three-by-three
linear system in variables x,y, and z. She tells us to:
- Take the first equation and solve it for x in terms of y and z.
- Take the second equation and do the same thing.
- Make a two-by-two system in y and z from the first two steps.
- Solve that system.
- Substitute the solutions for y and z back into the first equation and solve it for x.
This process will not, in general, work to solve a three-by-three system. Which of the
following constitutes a fatal flaw in our friend’s scheme?
(a) The process can work only if the system is consistent.
(b) The process completely ignores the third equation.
(c) The process does not use the addition method at any point.
(d) The process does not employ matrix morphing.
(e) The process can produce a solution only if the system is inconsistent.- There’s something else wrong with the process outlined in Question 146. What’s that?
(a) The third “bulleted” step will not actually give us a two-by-two system.
(b) The two-by-two system derived in the third step will be inconsistent.
(c) There is no way to derive an expression for x in terms of y and z.
(d) It will cause us to unwittingly divide by 0.
(e) It will cause us to unwittingly subtract an equation from itself.
xyf(x)g(x)Figure FE-16 Illustration for Final Exam
Question 145.