MATH122 Final: Final Exam Fall 2012
Document Summary
Instructors: semukhin (001, farenick (002, szechtman (003) Instructions: to receive full credit, show all of your work and explain all your steps. Use the back of each page if there is insuf cient space on the facing page is not available. Page 2: consider the vectors u = . In r3. (a) determine the lengths of u and v. (b) determine the cosine of the angle between u and v. (c) find a nonzero vector w that is orthogonal to both u and v. Page 3: consider the following system of linear equations: x1 + 2x2 + 2x3 = . X1 (a) determine all values of for which the linear system has a unique solution. (b) determine all values of for which the linear system has in nitely many solutions. 3 (a) calculate det a. (b) calculate a 1. (c) is b in the column space of a? (yes or no?) Without making numerical calculations, give reasons for your answer.
