Science:Math Exam Resources/Courses/MATH307/April 2006/Question 03 (b)
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Question 03 (b) 

Let be the set of all polynomials of degree at most 2. Show that the transformation is a linear transformation, where . 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2006/Question 03 (b)/Hint 1 
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Solution 

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Note that differentiation is a linear operator and some scalar c
and
Thus as
and
we see that T is a linear transformation. 