## MA1111 -- Michaelmas 2016

### Calendar:

Lecture Topics covered Notes
1 (27.09) Introduction, vectors, vector addition, and dot products Notes 1
2 (29.09) Cross products, multilinearity, and areas or parallelograms Notes 2
3 (30.09) Lines and planes in three-dimensional space Notes 3
4/5 (04.10,06.2026) Systems of linear equations, reduced row echelon form/Gauss-Jordan elimination,linear combinations/span, column space Notes 4/5
Tutorial 1 Tutorial 1
6 (11.10.2026) Matrix operations: Matrix addition, scalar multiplication, and matrix multiplication Notes 6
7 (13.10.2026) Elementary matrices and Matrix Inverses Notes 7
8 (14.10.2026) Determinants and Permutations Notes 8
9 (18.10.2026) Determinants and invertibility, transposes, minors and cofactors Notes 9
10 (20.10.2026) Determinants by Laplace expansion and inverses by adjoint matrices Notes 10
21.10.2016 Tutorial 2 Tutorial 2
11 (25.10.2016) 3x3 determinants, vector spaces Notes 11
12 (27.10.2016) Properties of vector spaces and subspaces Notes 12
13 (28.10.2016) Direct sums of vector spaces and spans of vectors Notes 13
14/15 (01/03.11.2016) Linear Independence and Bases Notes 14/15
(04.11.2016) Tutorial 3 Tutorial 3
16 (15.11.2016) Dimensions and coordinates Notes 16
17 (17.11.2016) Linear transformations Notes 17
18 (18.11.2016) Injective and surjective functions and transformations Notes 18
19 (22.11.2016) Matrix representations of linear transformations Notes 19
20 (24.11.2016) Compositions of linear transformations and change of basis Notes 20
(25.11.2016) Tutorial 4 Tutorial 4
(28.11.2016) Review Practice problems done in class
(01.12.2016) Further topics: Eigenvectors and eigenvalues
(02.12.2016) Further topics: Diagonalization
(06.12.2016) Application 1: A formula for Fibonacci numbers
(08.12.2016) Application 2: A rough idea of how Google works A detailed survey by David Austin
(09.12.2016) Tutorial 5 Tutorial 5
(13.12.2016) Review Day 1 Practice Problems in class
(15.12.2016) Review Day 2 Practice Problems in class
(16.12.2016) Review Day 3 Practice Problems in class

### Homework problems and solutions:

Homework 1, due October 6.

Homework 1 solutions.

Homework 2, due October 13.

Homework 2 solutions.

Homework 3, due October 20.

Homework 3 solutions.

Homework 4, due October 27.

Homework 4 solutions.

Homework 5, due November 3.

Homework 5 solutions.

Homework 6, due November 17.

Homework 6 solutions.

Homework 7, due November 24.

Homework 7 solutions.

Homework 8, due December 1.

Homework 8 solutions.

### Tutorial problems and solutions:

Tutorial 1.

Tutorial 1 solutions.

Tutorial 2.

Tutorial 2 solutions.

Tutorial 3.

Tutorial 3 solutions.

Tutorial 4.

Tutorial 4 solutions.

Tutorial 5.

Tutorial 5 solutions.

### Sample exams:

2016 Sample Exam.

2016 Sample Exam Solutions.

Old Sample Exam.

Old Sample Exam Solutions.

2013 Exam.

2013 Exam Solutions.

2012 Exam.

2012 Exam Solutions.

2011 Exam.

2011 Exam Solutions.

2010 Exam.

2010 Exam Solutions.