Science:Math Exam Resources/Courses/MATH221/April 2010/Question 01 (d)
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Question 01 (d) 

Let and Then the matrix U is an echelon form for A (you may assume this, you don't have to do the row reduction again.) Solve the equation 
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 

Find the reduced echelon form, that is, use row operations to set the entries above the pivot elements to zero. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. In order to solve we need to find the reduced echelon form. Starting with the echelon form , we first subtract the second row from the first row twice, , to obtain
Now we add the third row eight times to the first row, and subtract the third row three times from the second row, , , to obtain
In plain notation this means that
Fixing the pivot variables and solving the above for the remaining two variables we find that the solution to has the form
