Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 04 (b)
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Question B 04 (b) 

Let a=[1,2,1]. Consider the transformation defined by for all x in , where is the crossproduct in . Find the matrix A that corresponds to T. 
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 

Recall that we can formulate the matrix by understanding how the transformation affects the basis vectors. 
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. The columns of a linear transformation matrix, A, are populated by the transformed vectors of each of the basis vectors. In this case the first column of A will be , the second, , and the third, . By computing these cross products, we get, Therefore the linear transformation matrix A which corresponds to T is,
Notice if we wanted some sort of confirmation of our answer we can pick a random vector, say x=[3,4,7], compute and compute Ax and make sure they are the same thing. and which is indeed the same result. 