## Linear Algebra

This is the page for the 1H Linear Algebra course for academic year 2012-13. Model solutions to tutorial and homework problems will appear here after tutorials, plus some extra stuff you might find helpful along the way. If you need any more help with the course or you find any typos/mistakes either email me or come and see me in my office.

### Model Solutions:

• Week 2-Axioms of a vector space and formal proofs, the dot product (associativity, linearity, calculations) and introduction to $\mathbb{R}^{n}$.
Tutorial solutions here.
Homework model solutions here.
• Proof of Cauchy-Schwarz inequality here.
• Week 3-Cross Product, triple product, geometry of planes and lines and proofs using general products.
Tutorial solutions here.
• Homework model solutions here.
• Week 4- Lines and planes revisted, simulataneous equations and row reduced echelon form.
Tutorial solutions here.
• Week 5- Matricies and their properties (Inverses and Determinants).
• Week 6- More on matricies.
• Week 7- Using determinants and inverses (parallelograms and their properties).
Homework model solutions here.
• Week 8- Linear Independence, spanning sets, bases, the trace and Cramer's rule.
• Week 9- More on linear independence, spanning sets and bases including bases of alternative vector spaces.
• Week 10- Vector subspaces, rank, nullity , rank-nullity theorem, changes of basis and the dreaded magic sqaure question.