Linear Algebra I

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Work with linear transformations of R^n and their matrices.
• Calculate the determinants, invert and perform basic operations with matrices
• Solve systems of linear equations and apply this to other questions from Linear Algebra
• Apply Linear Algebra methods to geometric problems in R^3 and R^n.
• Find eigenvalues/eigenvectors of square matrices; diagonalize symmetric matrices

• Complex arithmetic
• Vectors in R^n: examples from R³, equations of lines and planes in R³.
• Systems of linear equations, Gaussian elimination.
• Matrix algebra: nxm matrices, sums, products, transpose, inverse of an nxn matrix, matrix equations.
• Determinants, cofactor definition of the inverse, proof that detA≠O if and only if A invertible.
• Properties of R^n, subspaces of R^n, span, null space and column space of a matrix.
• Linear independence of vectors in R^n.
• Scalar product and geometrical applications.
• Vector product and applications in R³.
• Linear transformations in R^n, examples in R² and R³.
• Eigenvalues and eigenvectors.

Throughout the module some theorems will be proved.

Lectures, problem classes and workshops

Formative

This is how we’ll give you feedback as you are learning. It is not a formal test or exam.

Exercise

• Assessment Type: Formative
• Feedback:
• Final Assessment: No
• Group Work: No

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.