Science:Math Exam Resources/Courses/MATH307/December 2006/Question 02 (c)
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Question 02 (c) 

Consider the matrix
(c) Find a basis for the left nullspace of 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 

Science:Math Exam Resources/Courses/MATH307/December 2006/Question 02 (c)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To find the basis of left nullspace, , we solve for This can be done by finding the row echelon form of Perform the following row operations:
and we get the matrix : Further row operations,
and interchanging row 2 and 3 gives us the row echelon form of the matrix as: From this we can see that only is a free variable. Solving this row echelon for homogeneous solution gives us : Thus a basis of is given by 