MA 260 LINEAR ALGEBRA
LECTURE 4
WING HONG TONY WONG
Last lecture, we nished discussing elementary row operations, Gauss-Jordan elimination
and reduced row echelon form.
1.3 Matrices and matrix operati
MA 260 LINEAR ALGEBRA
LECTURE 1
WING HONG TONY WONG
System of linear equations
This lecture is related to Sections 1.1 and 1.3.
Recall that an n-dimensional rectangular coordinate space is
Rn = cfw_(a
MA 260 LINEAR ALGEBRA
LECTURE 6
WING HONG TONY WONG
Last lecture, we nished discussing about matrix multiplication and other operations, like
taking transpose and trace. We also go through some of the
MA 260 LINEAR ALGEBRA
LECTURE 5
WING HONG TONY WONG
Last lecture, we discussed about addition, subtraction, scalar multiplication and multiplication of matrices.
1.3 Matrices and matrix operations
Let
MA 260 LINEAR ALGEBRA
LECTURE 2
WING HONG TONY WONG
System of linear equations
This lecture is related to Sections 1.1 and 1.2.
Last lecture, we gave the general form of a linear equation in n variabl
MA 260 LINEAR ALGEBRA
LECTURE 3
WING HONG TONY WONG
1.2 Reduced row echelon form and Gauss-Jordan elimination
Last lecture, we discussed how to use the three rules of elementary row operations on the
MA 260 LINEAR ALGEBRA
LECTURE 7
WING HONG TONY WONG
Last lecture, we nished the introduction to matrix inverses.
1.5 Elementary matrices and a method for nding A1
Recall that the three elementary row
MA 260 LINEAR ALGEBRA
LECTURE 8
WING HONG TONY WONG
Last lecture, we introduced elementary matrices, and performing an elementary row operation on A is the same as multiplying the corresponding elemen
MAT 260 LINEAR ALGEBRA
LECTURE 17
WING HONG TONY WONG
Last Wednesday, we dened determinants by cofactor expansion.
2.2, 2.3 Determinants by row reduction and column reduction and
properties of determi
MAT 260 LINEAR ALGEBRA
LECTURE 19
WING HONG TONY WONG
Last lecture, we proved how row operations will aect determinants of a matrix.
2.3 Properties of determinants
Theorem 1. (a ) Let B be a matrix ob
MAT 260 LINEAR ALGEBRA
LECTURE 13
WING HONG TONY WONG
Last lecture, we discussed about diagonal, upper triangular, lower triangular, symmetric
and skew-symmetric matrices.
2.1 Determinants by cofactor
MA 260 LINEAR ALGEBRA
LECTURE 11
WING HONG TONY WONG
1.6 More on linear systems and invertible matrices
If we are solving multiple equations Ax = b1 , Ax = b2 , . . . , Ax = bk at the same time,
then
MA 260 LINEAR ALGEBRA
LECTURE 9
WING HONG TONY WONG
Last lecture, we proved that there are a number of equivalent statements for saying that
A is invertible. We also introduced the method to nd the ma
MA 260 LINEAR ALGEBRA
LECTURE 10
WING HONG TONY WONG
1.6 More on linear systems and invertible matrices
If we are solving multiple equations Ax = b1 , Ax = b2 , . . . , Ax = bk at the same time,
then