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Table of Contents
Here you can find some lecture notes.
The main course web page contains more general information about the course.
MST10030 2016–2017 notes
These will appear as the course progresses.
Notes by lecture
- Lecture 1 - Tuesday 24 January 2017
- linear equations in two variables
- Lecture 2 - Thursday 26 January 2017
- linear equations in three or more variables
- systems of linear equations (first example)
- Lecture 3 - Tuesday 31 January 2017
- the augmented matrix of a system of linear equations
- the $(i,j)$ entry of a matrix
- elementary operations on a system of linear equations
- elementary row operations on a matrix
- Lecture 4 - Thursday 2 February 2017
- row echelon form
- reduced row echelon form
- Lecture 5 - Tuesday 7 February 2017
- leading variables and free variables
- solving a linear system in REF or RREF
- Gaussian elimination
- Lecture 6 - Thursday 9 February 2017
- Examples
- Inconsistent systems
- Deciding whether or not a system has infinitely many solutions
- Observations about Gaussian elimination and free variables
- Matrices: definition of a matrix and matrix entries
- Lecture 7 - Tuesday 14 February 2017
- Equality of matrices
- Addition and subtraction of matrices
- The zero matrix
- Scalar multiplication of matrices
- Row-column matrix multiplication
- An example of general matrix multiplication
- Lecture 8 - Thursday 16 February 2017
- Definition of matrix multiplication
- Examples
- Commuting and non-commuting pairs of matrices
- The identity matrix
- Lecture 9 - Tuesday 21 February 2017
- Properties of the identity matrix: proof
- The associative and distributive laws for matrix multiplication
- Lecture 10 - Thursday 23 February 2017
- Matrix equations
- Invertibility of a square matrix
- Uniqueness of inverses
- Lecture 11 - Tuesday 28 February 2017
- Solving $AX=B$ where $A$ is invertible
- The determinant and invertibility of a $2\times 2$ matrix
- Lecture 12 - Thursday 2 March 2017
- Midterm (no lecture)
- Lecture 13 - Tuesday 7 March 2017
- the transpose of a matrix
- $(AB)^T=B^TA^T$
- determinants of $n\times n$ matrices:
- minors
- cofactors
- the determinant of a $3\times 3$ matrix
- Lecture 14 - Thursday 9 March 2017
- the determinant of an $n\times n$ matrix
- Laplace expansion along any row or column
- the determinant of an upper triangular matrix
- properties of the determinant
- Lecture 15 - Tuesday 28 March 2017
- the effect of EROs on the determinant
- finding determinants using EROs
- the adjoint of a square matrix
- Lecture 16 - Thursday 30 March 2017
- a formula for the inverse of an $n\times n$ square matrix
- using EROs to find the inverse of a square matrix
- (column) vectors as instructions to move points
- Lecture 17 - Tuesday 4 March 2017
- the vector $\vec{AB}$ which moves point $A$ to point $B$
- the length $\|\vec v\|$ of a vector $\vec v$
- Scalar multiplication and direction
- Unit vectors
- Addition of vectors: the triangle and parallelogram rules
- Lecture 18 - Thursday 6 April 2017
- The dot product
- The geometric formula $\vec v\cdot\vec w=\|\vec v\|\,\|\vec w\|\cos\theta$
- Calculating angles
- Lecture 19 - Tuesday 11 April 2017
- The orthogonal projection of one vector onto another
- The cross product of vectors in $\mathbb{R}^3$: definition and properties
- The area of a triangle using the cross product
- Lecture 20 - Thursday 13 April 2017
- Geometry of the cross product: areas and volumes
- Planes in $\mathbb{R}^3$ and their normal vectors
- Lecture 21 - Tuesday 18 April 2017
- Parallel and orthogonal planes
- Examples: finding the equations of planes with various properties
- Lecture 22 - Thursday 20 April 2017
- The distance from a point to a plane
- The distance between planes
- The parametric equation of a line
Lecture slides
Here are links to the slides I used in the lectures. They cover much the same material as the notes above, and are provided in response to a student request.
- Lecture 12 - no slides (midterm)
MST10030 2015–2016 notes
These have now been archived as a PDF file.
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