MAT 260 LINEAR ALGEBRA
LECTURE 28
WING HONG TONY WONG
4.2 Subspaces
Let V be a vector space. A nonempty subset W of V is a subspace of V if
(1) the addition and scalar multiplication dened in W are in
MAT 260 LINEAR ALGEBRA
LECTURE 22
WING HONG TONY WONG
2.2, 2.3 Determinants by row reduction and column reduction and
properties of determinants
Remember that we can obtain the determinant of matrix A
MAT 260 LINEAR ALGEBRA
LECTURE 20
WING HONG TONY WONG
2.1 Determinants by cofactor expansion
The determinant of a 1 1 matrix is the entry itself. The determinant of a 2 2 matrix
ab
ab
ab
is ad bc. We
MAT 260 LINEAR ALGEBRA
LECTURE 19
WING HONG TONY WONG
1.7 Diagonal, triangular, and symmetric matrices
A square matrix A is a diagonal matrix if aij = 0 for all i = j , i.e. all entries outside the
ma
MAT 260 LINEAR ALGEBRA
HOMEWORK 1
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each prob
MAT 260 LINEAR ALGEBRA
LECTURE 1
WING HONG TONY WONG
Review Brief introduction to set notations
Most of modern mathematics are built upon set theory. Hence, to learn modern subjects
such as linear alg
MAT 260 LINEAR ALGEBRA
HOMEWORK 5
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each prob
MAT 260 LINEAR ALGEBRA
HOMEWORK 4
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each prob
MAT 260 LINEAR ALGEBRA
HOMEWORK 2
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each prob
MAT 260 LINEAR ALGEBRA
HOMEWORK 3
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each prob
MAT 260 LINEAR ALGEBRA
LECTURE 2
WING HONG TONY WONG
1.1 System of linear equations
An n-dimensional rectangular coordinate space is
Rn = cfw_(a1 , a2 , . . . , an ) : a1 , . . . , an R.
An element in
MAT 260 LINEAR ALGEBRA
LECTURE 3
WING HONG TONY WONG
1.2 Gaussian Elimination
Recall from the last lecture that a system of linear equations
a11 x1 + a12 x2 + + a1n xn = b1 ,
a21 x1 + a22 x2 + + a2n x
MAT 260 LINEAR ALGEBRA
LECTURE 16
WING HONG TONY WONG
1.6 More on linear systems and invertible matrices
Theorem 1. A system of linear equations has zero, one or innitely many solutions. There
are no
MAT 260 LINEAR ALGEBRA
LECTURE 13
WING HONG TONY WONG
1.5 Elementary matrices and a method for nding A1
Recall that the three elementary row operations of a matrix A are
1. Switch row i and row j ;
2.
MAT 260 LINEAR ALGEBRA
LECTURE 4
WING HONG TONY WONG
1.2 Gaussian elimination
Once again, the recipe for solving a system of linear equations is the following:
(1) Set up an augmented matrix.
(2) Perf
MAT 260 LINEAR ALGEBRA
LECTURE 25
WING HONG TONY WONG
4.1 Real vector spaces
Before we start introducing the denition of vector space, we need to rst understand the
concept of addition and scalar mult