MAST10007 Linear Algebra Semester 1, 2017 Assignment 3 Due: 12 noon on Monday, March 27. Late assignments will not be accepted. You should show all working for all your answers. Please leave your assignment in your tutor's box located near the north entrance to the Peter Hall building. Make sure that you have written your name, your student number, your tutor's name, and your tutorial time on the front page. From the questions below, one will be chosen for marking. Please note that some marks will be allocated for properly setting out your solutions and correct use of notation. 1. Consider the following matrix (which has entries from C): 2 3 i 2i 1 1 i 5 M =4 1 2 i 1 i (a) Calculate the determinant of M by using row operations to reduce to upper triangular form. (b) Calculate the determinant of M by using a cofactor expansion along the third column. 2. For the following matrix, evaluate det(A) and use your answer to give the values of t 2 R for which A is invertible. 2 3 2 t 0 0 3 6 0 t t 0 7 7 A=6 4 0 t 2t 0 5 t 2 0 0 t+3 3. Consider the following three points in R3 : P ( 1, 1, 0), * * * Q(1, 5, 6), R(3, 1, 4) * (a) Calculate P Q P R and P Q P R. * * * (b) Find the values of x 2 R for which P R + xQR is perpendicular to P R. (c) Use the cross product to find the area of the triangle with vertices P , Q and R. Mathematics and Statistics University of Melbourne