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assignment 1

# assignment 1 - (v ﬁnd the transpose of your matrix A in...

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Lin Alg Assignment 1, Due Fri Oct 16 @ 4:00 pm F09 TA Name: Tutorial Day: and Time: Group Members (Last Name and Initials): (1) (2) (3) The purpose of this assignment is for you to develop some familiarity with the Matlab software. This assignment is to be done individually, but submit one paper print-out per group using this page as a cover, with the student names, tutorial day and time, and TA clearly labeled at the top in the space provided. You must use the “diary” set-up for this assignment, and print and submit the diary text file. Clearly label the questions you are doing; make sure your answers to the questions are explicit . A short intro to matlab is available under the assignments link on WebCT. 1. (1 mark each) Use Matlab commands to: (i) define the identity matrix of order 4; (ii) define the zero matrix of size 3 × 5; (iii) augment a 4 × 4 matrix A of your choice by a 4 × 1 column matrix b of your choice; (iv) retrieve the 23 entry in your matrix
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Unformatted text preview: (v) ﬁnd the transpose of your matrix A in part (iii) above. 2. (2 marks each) Solve the following linear systems (if possible, if not state why the system is inconsistent), by row reduction : ( i ) 2 x 1 + 2 x 2-x 3-3 x 5 = 0 3 x 1-x 2 + 2 x 3-x 4-x 5 = 0 x 1 + x 2-x 5 = 0 2 x 3 + 2 x 5 = 0 ( ii ) w + x-2 y + z =-3 3 w + 2 x-y + 3 z =-1-w + 3 x + y-4 z = 12 2 x + y-4 z = 10 3. (3 marks) Solve the system in 2(ii) above by the method of matrix inversion . Can you use this method to solve the system in 2(i)? Justify your answer. 4. (2 marks each) Verify the following properties: (i) ( AB )-1 = B-1 A-1 when A,B are distinct invertible 3 × 3 matrices of your choice. (ii) tr ( CD ) = tr ( DC ) when C is a 4 × 2 and D is a 2 × 4 matrix of your choice. (iii) ( A T )-1 = ( A-1 ) T for your matrix A above. (iv) A ( B + C ) = AB + AC for any 3 × 3 matrices of your choice....
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