As always, you should rework (not just read) the example I worked in class. If you cannot rework the example I worked in class correctly, then you do not understand the method and will not be able to do the assigned problems correctly.

On the problems below, make sure you use Gauss elimination EXACTLY as it was presented in class and NOT in a manner that you might have learned in a different course.

1. Use Gauss elimination as presented in class to solve the system:

   4 7 12 44 62 140 80 –55 354

   x1 x2 x3

   =

   60 516 –702

   Answer:

   x₁ = 10,   x₂ = 8,   x₃ = –3

2. Use Gauss elimination as presented in class to solve the system:

   5 12 7 –3 –15 –44 –12 13 40 144 11 –37 30 –40 150 17

   x1 x2 x3 x4

   =

   20 220 –1332 3668

   Answer:

   x₁ = 20,   x₂ = –15,   x₃ = 16,   x₄ = 4

   
   Do the following AFTER Friday's lecture.

3. If a computer takes 30 seconds to solve a 60 x 60 system by Gauss elimination, estimate how long will it take to solve a 300 x 300 system.
   Answer:    About 62.5 minutes

4. If a computer takes 6 seconds to solve a system of order 200 by Gauss elimination, estimate how long will it take to solve a system of order 5000.
   Answer:    About 26 hours

5. Suppose a computer program for Gauss elimination requires 0.75 seconds to solve a system of 80 equations for 80 unknowns. Estimate how long it will take to solve a system of order 2,000.
   Answer:   About 3.25 hours

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