Science:Math Exam Resources/Courses/MATH152/April 2010/Question A 20
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Question A 20 |
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Let T be a linear transformation from 2D to 3D such that
and
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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 |
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Recall that transformations are linear and hence obey the property T(ax)=aT(x) and T(x+y)=T(x)+T(y). Is there anyway that we can represent the vector we want in terms of the vectors we know transformation information for? |
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.
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. Notice that I can write [0,1] in terms of the other two vectors [2,3] and [1,1] via, Now transformation are linear. This means that T(ax)=aT(x) and T(x+y)=T(x)+T(y). Therefore, Therefore |