Science:Math Exam Resources/Courses/MATH152/April 2010/Question A 21
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Question A 21 

Let T be a linear transformation from 2D to 3D such that
and

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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

We already know the transformation of one of the basis vectors from A20. If we knew the transformation on the other basis vector, how could we form the matrix? 
Hint 2 

Recall that the columns of a transformation matrix are the transformations of the basis vectors. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. Just like in A20, we can write, Now transformation are linear. This means that T(ax)=aT(x) and T(x+y)=T(x)+T(y). Therefore, Therefore and from A20 we have, so therefore where we recall that the columns of the transformation matrix are just the transformation of the basis vectors. 