Topics we've covered in 535, Chapters 1-3; things you need to know.

Basic operations with matrices; properties of the operations
Types of matrices: nonsingular, singular, symmetric, skew symmetric,
                   diagonal, triangular, strictly upper/lower triangular
Inverses & transposes: properties & computation
Use of partitioned matrices
Elementary row operations and elementary matrices: definitions & properties
Row echelon form of matrices; reducing to rref
Solution of homogeneous systems (Ax=0)
Vector spaces: definition and basic properties
Subspace: definition & how to check if a set is a subspace
Examples of vector spaces & subspaces
Linear combinations, spanning, and linear independence
Definition of a basis & properties of bases
Dimension of a vector space
Associating a matrix to (ordinary) vectors, and what the matrix tells us
 about spanning, linear independence, being a basis
The row space, column space, and null space of a matrix: definition & properties


We skipped Sections 2.5,2.6,3.5, and we only got through the first half
 of Section 3.6 (and none of 3.7-3.9)