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.