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.