Science:Math Exam Resources/Courses/MATH307/December 2010/Question 02 (a)
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Question 02 (a) 

Suppose that (a) Write down a basis for R(A). 
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 rows in the rref(A) with leading 0s and then a 1 (ie pivot columns) correspond to columns that belong to the basis. 
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. Given rref() all we will need to find are the pivot columns in and find those same columns in the matrix , giving . Columns 1, 3, and 5 correspond to the pivot columns in rref(A) so columns 1, 3, and 5, give the basis for . Hence, a basis of is 