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

Let be the set of all polynomials of degree at most 2. Show that is a vector space and show that form a basis of . Express the function in a vector form using B as the basis. 
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Hint 

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

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Please rate my easiness! It's quick and helps everyone guide their studies. If is a vector space then the axioms must hold true
We can also think of to be in
such that commutative and associate properties are also satisfied. To show that B is a basis, we have to show that it spans and are linearly independent If we think of to be in then we can immediately identify the basis for Basis of We can use this result and build the basis of such that . Therefore
