MATH 551 Final: MATH 551 KSU Final Exam s01

• School: Kansas State University
• Department: Mathematics
• Course: MATH 551
• Professor: All

Document Summary

Show all your work in the space provided under each question. Each problem is worth 10 points: solve the system of equations. x + 2y 3z = +5. 5x + 3y 5x = 11: given a = . , nd a 1: consider the polynomials p1(x) = 1, p2(x) = x + 1 and p3(x) = (x + 1)2 which form a basis for p2. What are the coordinates of q(x) = x2 + 1 with respect to this basis: find the lu decomposition of the matrix a = . 4 2 7 page 2: de ne t : r3 r3 by t (v) = av where a = . Find a basis for the image of t and a basis for the nullspace of t . 1 3 4: use the gram-schmidt process to nd an orthogonal basis for the subspace of r4 spanned by. 2: on [ 1, 1] de ne f (x) = (1 if x 0.