School of Mathematics and Statistics
Assignment 2
MATH1014: Introduction to Linear Algebra Semester 2, 2022
This individual assignment is due by 11:59pm Friday 16 September 2022, via
Canvas. Late assignments will receive a penalty of 5% per day until the closing date.
A single PDF copy of your answers must be uploaded in Canvas at
https://canvas.sydney.edu.au/courses/44706. It should include your SID. Sub-
missions can be overwritten until the due date. Please do not include your name in
any area of your assignment. The School of Mathematics and Statistics encourages
some collaboration between students when working on problems, but students must
write up and submit their own version of the solutions.
This assignment is worth 10% of your final assessment for this course. Your answers should be
well written, neat, thoughtful, mathematically concise, and a pleasure to read. Please cite any
resources used and show all working. Present your arguments clearly using words of explanation
and diagrams where relevant. After all, mathematics is about communicating your ideas. This
is a worthwhile skill which takes time and effort to master. The marker will give you feedback
and allocate an overall letter grade and mark to your assignment using the following criteria:
Copyright c? 2022 The University of Sydney 1
Assignment Questions:
1. Consider the vector n = and the points A = (1,?1, 3) and B = (1, 3, 5) in R3.
(a) Give the parametric vector equation of the straight line L through A and B.
(b) Give the Cartesian equation of the plane P through A, which n is normal to.
(c) Does the line L lie in the plane P? Justify your answer.
2. Consider the lines L1 and L2 in R3 given by the parametric equations