Upon successful completion of the course, students will be able to:
- Solve application problems of systems of linear equations.
- Perform the operations of addition, scalar multiplication, multiplication, and find the inverses and transposes of matrices.
- Calculate determinants using row operations, column operations, and expansion down any column or across any row.
- Prove algebraic statements about vector addition, scalar multiplication, inner products, projections, norms, orthogonal vectors, linear independence, spanning sets, subspaces, bases, dimension and rank.
- Find the kernel, rank, range and nullity of a linear transformation.
- Calculate eigenvalues, eigenvectors and eigenspaces.
- Determine if a matrix is diagonalisable, and if it is, diagonalise it.