MATH 125 Study Guide - Final Guide: Row Echelon Form, Unit Vector, Augmented Matrix
Document Summary
Additional practice problems for midterm (up to 2. 2) Note: some of the solutions here are just sketches (the main purpose is to enable you to check your own answers). In particular, row reduction of matrices is omitted completely. In your exam, however, you should show all your work, and give suitable justi cation for your answers. When row reducing a matrix, you should clearly indicate which row operations have been applied at each step of the process: let. Solution: a) i) 4~v 3~u = : ||~v|| = 3. iii)||~u|| = 2, ~v ~u = 4, d(~v, ~u) = 19. 11: no, because ~v ~u = 4 6= 0, no, because they are not scalar multiples of one another, i. e. , we cannot nd a scalar c such that c . 1 (c cannot be both 1/2 and 0: no, because ||~v|| = 3 6= 1. 3 )k. the vectors ~a and ~b are othogonal.
