MATH152 April 2013
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Question A 17
Decide if the transformation T, which we will define below, is a linear transformation of not. Jusify your answer.
Let be a transformation that maps into
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!
Remember that a transformation is linear if it satisfies
where x and y are vectors and c is a real number.
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Let and a real number. Then
and so the map is not linear because the second rows do not match.
Alternatively, one could show that
and once again, we see that the map is not linear. The moral of this question is that the one in the middle row is causing the map to not be linear.
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