MATH307 December 2012
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q4 (e) • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) • Q6 (f) •
Question 01 (c)
In this question we will work with polynomials of degree 3 written
(c) The coefficient vector satisfies an equation of the form Ba=b when the graph of p(x) passes through the points (0,1), (1,2) and (2,2). Write down the matrix B and the vector b.
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We have three points which should generate three linear equations for the unknown coefficients. How can we turn this into a matrix?
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passes through and
Mathematically, for p(0)=1,
and for p(2)=2,
The systems above can be written in a form of
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