MATH 240 Lecture Notes - Lecture 14: Linear Map, Gaussian Elimination

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 240
• Professor: Michael Monagan

Document Summary

1. 8 additional exercise 1: find all vectors x r3 that are mapped into the zero vector by the linear transformation t (x) = ax where a is the matrix below. This set of vectors is called the kernel of t and is denoted ker(t ). Solution: the vectors mapped to 0 are the solutions of ax = 0. Now solving bx = 0 for i get. 1. 8 additional exercise 2: let a be an m n matrix and b rm. Consider the linear function t : rn rm given by t (x) = ax + b. Show that t is not a linear transformation when b 6= 0. Solution: we just need to nd one counter example. If t is a linear transformation then t (0) should be the 0 vector. But t (0) = a0 + b = b which is not the 0 vector. 2. 1 additional exercise: let a and b be two 2 2 matrices.