MATH 307 Midterm: MATH 307 2012 Winter Test 1

• School: UBC
• Department: Mathematics
• Course: MATH 307
• Professor: all

Document Summary

A matlab/octave formula sheet is provided on the last page. In this question we will work with polynomials of degree 3 written p(x) = a1x3 + a2x2 + a3x + a4 (a) [4 pts] The coe cient vector a = [a1, a2, a3, a4]t satis es an equation of the form aa = 0 when the slopes of p(x) at x = 0 and x = 2 are zero. Write down the matrix a. (b) [4 pts] Show that dim(n (a)) = 2 and nd a basis a1, a2 for n (a). (c) [4 pts] The coe cient vector a = [a1, a2, a3, a4]t satis es 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. Page 3 of 12 pages (d) [4 pts]