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Department of Mathematics and Statistics

Summer Semester, 2015

MAST10007 Linear Algebra

Lecture Slides

These notes are not intended as a textbook.

They are an accompaniment to the lectures.

You need to take notes during the lectures.

These slides have been printed on one side so that you can use

the blank side for note-taking.

This compilation has been made in accordance with the provisions of Part VB of the Copyright Act

for the teaching purposes of the University. This booklet is for the use of students of the University of

Melbourne enrolled in the subject MAST10007 Linear Algebra.

These notes are not intended as a textbook.

They are an accompaniment to the lectures.

You need to take notes during the lectures.

These slides have been printed on one side so that you can use

the blank side for note-taking.

This compilation has been made in accordance with the provisions of Part VB of the Copyright Act

for the teaching purposes of the University. This booklet is for the use of students of the University of

Melbourne enrolled in the subject MAST10007 Linear Algebra.

Topic 1: Linear equations

[AR 1.1 and 1.2]

MAST10007 Linear Algebra

Topic 1:

Linear equations

Topic 2:

Matrices and determinants

34

Topic 3:

Euclidean vector spaces

76

Topic 4:

General vector spaces

173

Topic 5:

Linear transformations

208

Topic 6:

Inner product spaces

252

Topic 7:

Eigenvalues and eigenvectors

One of the major topics studied in linear algebra is systems of linear

equations and their solutions.

2

288

We will study an efficient and systematic technique for solving

simultaneous linear equations.

1.1. Systems of equations. Coefficient arrays. Row operations.

1.2. Reduction of systems to row-echelon form and reduced row-echelon

form.

1.3. Consistent and inconsistent systems. Infinite solution sets.

2

1

1.1 Systems of equations, coefficient arrays, row operations

Linear...