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Curricular information is subject to change
After successful completion of this module, a student should be able to:
- Define and discuss the main concepts related to vector spaces and linear transformations.
- Construct examples of vector spaces, subspaces and linear transformations.
- Determine if a given set of vectors is linearly independent, a spanning set, a basis.
- Determine if a subset of a vector space is a subspace.
- Determine bases of the row space, column space and null space of a given matrix.
- Determine the rank and nullity of a given matrix.
- Compute the characteristic polynomial, eigenvalues and eigenvectors of a given matrix.
- Determine whether or not a matrix can be diagonalized.
- Compute with coordinatizations of vectors after a choice of basis.
- Compute the change of basis matrix for given bases of a vector space.
- Compute the matrix of a linear map with respect to a choice of bases.
- Determine kernel and image of a linear map.
- Determine if a linear map is injective, surjective, bijective.
- Determine rank and nullity of a linear map.
Brief revision of Gaussian elimination and Gauss-Jordan elimination, vector spaces over a field, subspaces, spanning sets, linear independence, bases, dimension, coordinate spaces, matrix techniques, row space, column space, null space, rank and nullity of a matrix, eigenvalues, eigenvectors, diagonalization, revision of functions on sets and their properties, linear transformations, kernel and image, isomorphisms, matrix of a linear transformation, vector space of linear transformations, change of bases for matrices of linear transformations, rank and nullity of a linear transformation, quotient spaces, dimension formula, first isomorphism theorem, rank-nullity theorem.
Student Effort Type | Hours |
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Lectures | 24 |
Tutorial | 12 |
Autonomous Student Learning | 76 |
Total | 112 |
This course relies heavily on the theory of systems of linear equations. Anyone taking this course should have a good grasp of Gaussian elimination, Gauss-Jordan elimination, results relevant to solving systems of linear equations and basic matrix algebra including computing determinants and matrix inverses. A working knowledge of integer, rational, real and complex numbers and the differences between them is desirable. Students should have previously taken and passed MST10030 Linear Algebra I, MATH10200 Matrix Algebra or an equivalent course.
Description | Timing | Component Scale | % of Final Grade | ||
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Not yet recorded. |
Resit In | Terminal Exam |
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Autumn | Yes - 2 Hour |
• Group/class feedback, post-assessment
Not yet recorded.
Name | Role |
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Ms Claire Mullen | Tutor |