## ALGEBRA with GEOMETRY

### STUDENT INFO for E&IT

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Lecture notes on

fields and complex numbers

complex numbers

polynomials

groups,

vector spaces,

linear mappings,

matrices

matrices and linear mappings

Jordan block matrices.

Problem sheets for

Tutorial 1. Complex numbers - basics.

Tutorial 2. Complex numbers - continued.

Tutorial 3. Polynomials.

Tutorial 4. Groups.

Tutorial 5. Vector spaces. Subspaces.

Tutorial 6. Basis. Dimension.

Tutorial 7. Matrices.

Tutorial 8. Systems of equations.

Tutorial 9. Determinant. Inverse matrix.

Tutorial 10. Linear mappings. Matrices of linear mappings

Tutorial 11. Change-of-basis matrix

Tutorial 12. Eigenavalues. Diagonal matrices

Hints for old problems from test 1 here.

Hints for old problems from test 2 here.

Midterm 1, spring semester 2010 - solutions.

Midterm 1, fall semester 2010 - solutions.

Midterm 2, fall semester 2010 - solutions.

Midterm 1, fall semester 2011 - solutions.

Sample Jordan-block problems with detailed solutions.

Sample 12 Jordan-block problems with answers (not solutions!). I only included Jordan matrix, since there are infinitely many correct change-of-basis matrices. When you find your own change of basis matrix you can easily verify your solution by matrix multiplication.

You will find here, here,
here, here and also here solutions to some old final exams.