Linear Algebra Notes
Chapter 19 KERNEL AND IMAGE OF A MATRIX
Take an n m matrix a11 a21 A= . . . an1 and think of it as a function A : Rm - Rn . The kernel of A is defined as ker A = set of all x in Rm such that Ax = 0. Note that ker A lives in Rm . The i
McGill University Math 270: Applied Linear Algebra
CHAPTER 2:
MATRICES AND DETERMINANTS
1 Matrix Algebra
Suppose given two matrices two matrices are equal,
A = [aij ] and B = [bij ]. The
A = B,
if and only if
They have the same dimensions; All correspond
APPLIED LINEAR ALGEBRA - THE LECTURE NOTES FOR MATH270 (2010)-Fall
APPLIED LINEAR ALGEBRA
JIAN-JUN XU
Department of Mathematics and Statistics, McGill University
Kluwer Academic Publishers Boston/Dordrecht/London
Contents
1. SOLUTIONS OF SYSTEMS OF LINEAR
McGill University Math 270-2010 Fall: Applied Linear Algebra Written Assignment 3: due on Monday, Nov. 15, 2010, hand in in class. 1. Linear transformations: (a) Let Pn be the space of polynomials of degree less than or equal to n in a variable x with rea
McGill University Math 270-2010 Fall: Applied Linear Algebra Written Assignment 2: due on Monday, Oct. 18, 2010 1. Vector Space (a) In vector space P2 , let (S) be the set consisting of three quadratics: 1 + 2x + 3x2 , 4 + 5x + 6x2 , 7 + 8x + 9x2 .
Does
McGill University Math 270-2010 Fall: Applied Linear Algebra Written Assignment 1: due on Monday, Oct. 4, 2010 1. Give (3 5) matrix: A=
1 -2 2 -4 3 -6
0 1 1
1 -1 0 -1 1 0
.
(a) Determine the dimension of the subspaces col(A) and row(A); (b) Find the basis
APPLIED LINEAR ALGEBRA (McGill University MATH-270 (2010-Fall) Instructor: Prof. Jian-Jun Xu "McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism, and other academic off