Science:Math Exam Resources/Courses/MATH221/December 2007/Question 02
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Question 02 

Find the inverse of the matrix

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 

Science:Math Exam Resources/Courses/MATH221/December 2007/Question 02/Hint 1 
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. We are going to use GaussJordan elimination. Append the identity matrix to B,
and proceed to rowreduce. First, we multiply the first row by 1/2. Second, eliminate the 3 and 5 entries in the third row by subtracting 3 times the second row from the third, and subtracting 5 times the fourth row from the third. After these steps, we obtain
The last step is to add the third row to the first row. We find
Therefore, by GaussJordan elimination, we have found
