Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 01 (c)
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Question B 01 (c) 

Three friends, Hartosh, Mark and Keiko decide to paint houses over the summer. Hartosh paints twice as fast as Mark. Hartosh and Keiko paint a home with six rooms in 8 hours. All three together paint a home with 14 rooms in 16 hours. (c) Solve the system above using Gaussian elimination on the augmented matrix. How many rooms can each of the three friends paint in an hour? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Remember that Gaussian elimination uses row operations to create a lower triangular matrix. What are the pivots? How do we make entries below those pivots vanish? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. From B1(b) we have that the augmented matrix is
Finally then, by continuing Gaussian elimination, we want to make the pivot in the third row (the number in the third column) have a value 1. We therefore multiply the third row by 1/8 to get
