MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 1.7: Linear independence
Lay 1.7: Linear independence
MATH1113
Linear Algebra Slides
In linear algebra, a family of vectors is linearly independent if none of
them can be written as a linea
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 8 Solutions
Question 1. Eigenvalues and Eigenvectors
(10 mar
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 9 Solutions
Question 1. Eigenvalues and Eigenvectors
(10 mar
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 9
Due at 5:00pm on Wednesday, October 24.
Your solutions sh
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 6
Due at 5:00pm on Wednesday, October 3.
Your solutions sho
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 4
Due at 5:00pm on Wednesday, August 29.
Your solutions sho
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 4 Solutions
Question 1. Subspaces
(2 marks)
Are the followin
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 3 Solutions
Question 1. Linear independence/dependence
(2 ma
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 5
Due at 5:00pm on Wednesday, September 26.
Your solutions
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 2 Solutions
Question 1. Span of column vectors
4 5 1 8
3 7 4
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 1
Due at 5:00pm on Wednesday, August 8.
Your solutions shou
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 1.3: Vector equations
Key ideas
Lay 1.3: Vector equations
MATH1113
Linear Algebra Slides
in this lecture, we will introduce the notion of vectors in Rn (the set of
ordered n-tuples of real
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Introduction
Reference Material
Main resources
MATH1113
Linear Algebra Slides
Algebra textbook
David Lay, Linear Algebra and its Applications, Addison-Wesley
The 4th Edition, or the 3rd Edition
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 1.5: Solution Sets of Linear Equations
Lay 1.5: Solution Sets of Linear Equations
MATH1113
Linear Algebra Slides
In this lecture, we will write the general solution in (parametric) vector
f
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 3.2: Properties of determinants
Row operations
Lay 3.2: Properties of determinants
In this section, we will discuss the eects of elementary row operations on
the determinant of a matrix. On
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 3.2: Properties of determinants
Row operations
Lay 3.2: Properties of determinants
In this section, we will discuss the eects of elementary row operations on
the determinant of a matrix. On
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 2.9: Dimension and rank
Coordinates relative to a basis
Lay 2.9: Dimension and rank
Denition
Suppose B = cfw_v1 , . . . , vp is a basis of a subspace H.
If v H and
v = c1 v1 + + cp vp
MATH
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Lay 2.2: The Inverse of a matrix
Lay 2.2: The Inverse of a matrix
MATH1113
Linear Algebra Slides
Key idea
The inverse of a real number a = 0 is denoted by a1 and satises
aa1 = a1 a = 1.
Lecture
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 1 Solutions
Question 1. Solving linear systems
(5 marks)
A l
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Assignment 7
Due at 5:00pm on Wednesday, October 10.
Your solutions sh
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Tutorial 1 Solutions
Question 1. Discussion Linear algebra
True or fals
Instructor(s): Dr David Ridout and Dr Bryan Wang
Mathematical Sciences Institute
Australian National University
Second Semester, 2012
MATH1113, Mathematical Foundations for Statistics
Tutorial 4
Question 1. Discussion Linear algebra
True or false (Justify
MATH1113 Linear Algebra Slides
MATH1113 Linear Algebra Slides
Introduction
Linear Algebra overview
Lay 1.1: Systems of linear equations
Linear equations
Systems of linear equations
Solution of a system of linear equations
Examples
Equivalent systems
Strat