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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? 
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 

Apply the definition of linearity to check if the given function is indeed linear. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The statement is true. In order to prove T is a linear transformation, we need to show that for any and vectors , the properties
are satisfied . Let us check these properties:
Therefore, is a linear transformation. 