Unformatted text preview: 2. (a) Use Lagrange formula to ﬁnd the unique polynomial of degree ≤ 2 which passes through the three points (0,1), (1,2) and (1,3). (b) Do some algebra to write the polynomial as follow: p ( x ) = a 2 x 2 + a 1 x + a (c) What is the Vandermonde matrix X associated with this interpolation problem? (d) Check that check that the vector [ a , a 1 , a 2 ] T is a solution of X a a 1 a 2 = 1 2 3 3. We have seen in class that, if n points are given, then there is a unique polynomial of degree ≤ n1 going through these points. Take two points, let say (0,0) and (1,1). (a) What is the only polynomial of degree ≤ 1 going through these two points? (b) Find two diﬀerent polynomials of degree 2 going through these two points. 1...
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 Spring '10
 THOMAS
 #, Complex number, 5 digits

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