on the polynomials in x:

is the integral of p(x)q(x) dx from -1 to 1. A basis for the quadratic polynomials is {1, x, x^2}. Use the Gram-Schmidt process to convert this into an orthonormal basis with respect to this inner product. [Section 5.5 touches on this also.] 5.3 # 4, 10, 16!, 18!, 20!, 28, 31!, 34!, 37! Extra problem on projections: http://www.math.umass.edu/~markman/math235_spring11_html/extra-problem-least-squares.pdf 5.5 # 2, 4, 8, 9! REVIEW: ***** 5PM Monday 8 December 2014 in the lowrise (LGRC A310) ***** FINAL EXAM: ***** 10:30AM Wednesday 10 December 2014 in Totman Gym ***** ==================================================================== ==================================================================== (Old) Practice Exam: http://www.gang.umass.edu/~kusner/class/pracexam2.pdf Also, please think about this problem: Suppose we want to compute the exponential of a matrix exp(A) = I + A + A^2/2 + ... + A^k/k! + ... - how does having a basis of eigenvectors for A, along with their corresponing eigenvalues, help us?! Practice final solutions (not sure I like the sound of that): http://www.math.umass.edu/~kusner/prac235finalsols.pdf HAVE A GREAT SUMMER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ==================================================================== ==================================================================== Answers to T/F questions from the end of each chapter for Bretscher _Linear Algebra, 3E [of course, it is YOUR job to figure out why]. !!!!!!!!!!!!!!!!!! Warning: 4E has changed !!!!!!!!!!!!!!!!!!!!!!!!! ==================================================================== ============================no guarantees=========================== ==================================================================== Chapter 1 1 T 2 F 3 F 4 T 5 T 6 F 7 F 8 F 9 T 10 T 11 F 12 F 13 T 14 T 15 T 16 T 17 T 18 T 19 F 20 F 21 F 22 T 23 F 24 T 25 F 26 T 27 F 28 F 29 F 30 T 31 T 32 T 33 F 34 T 35 F 36 T 37 T 38 T 39 F 40 F 41 T 42 T 43 T 44 F 45 T Chapter 2 1 T 2 F 3 T 4 T 5 F 6 T 7 F 8 F 9 T 10 T 11 F 12 T 13 T 14 T 15 T 16 T 17 F 18 T 19 F 20 T 21 F 22 T 23 F 24 T 25 T 26 T 27 T 28 F 29 F 30 T 31 F 32 F 33 T 34 T 35 T 36 T 37 F 38 T 39 F 40 T 41 T 42 F 43 T 44 F 45 T 46 T 47 F 48 F 49 F 50 F 51 F 52 T 53 T 54 T [over the COMPLEX NUMBERS; what about REAL NUMBERS?] 55 T 56 T Chapter 3 1 F 2 T 3 T 4 F 5 T 6 F 7 T 8 F 9 T 10 F 11 T 12 T 13 F 14 T 15 T 16 F 17 T 18 T 19 T 20 T 21 F 22 F 23 T 24 T 25 T 26 T 27 F 28 F 29 T 30 T 31 T 32 F 33 F 34 T 35 F 36 T 37 T 38 F 39 F [although there is a natural way to realize it as a subspace!] 40 T 41 T 42 F 43 T 44 T 45 T 46 T 47 T 48 F 49 T 50 T 51 F 52 T 53 F [this one is tricky ;] ==================================================================== ============================no guarantees=========================== ====================================================================