MATH 133 Study Guide - Final Guide: Row And Column Spaces, Invertible Matrix, Elementary Matrix

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 133
• Professor: John Stix

Document Summary

Student number (mcgill id: print your name and student number in the above boxes. Instructions: you can use both the front and back of each page, as well as the work-continuation pages at the end, for your answers, show all your work to obtain full marks, this is a closed book exam. Notes, dictionaries of any kind, calculators, cellphones or any other devices, are not permitted. June 1, 2016: (10pts) (a) find the values of k for which the system. = 4 x+2y + (k2+4)z = k has (i) a unique solution (ii) no solution (iii) in nitely many solutions. (b) where the system has in nitely many solutions, write these in parametric form. June 1, 2016: (10pts) suppose a is a 3 3 matrix such that det a = 2. Find det b in each of the following cases: (a) b = 1 (b) b = 3adj(2a 2)