MATH221 December 2008
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Question 08 (b)
True or false (explain your answer): Let be the transformation of given by . Then is a linear transformation.
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?
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Apply the definition of linearity to check if the given function is indeed linear.
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The statement is true. In order to prove T is a linear transformation, we need to show that for any and vectors , the properties
- , and
are satisfied .
Let us check these properties:
Therefore, is a linear transformation.