• The SpaceR²
• The SpaceR³
• The SpaceRⁿ

• Matrices
• Operations with Matrices

• Gaussian Elimination
• Using Elementary Row Operations to Determine A−1
• Introduction to Linear Systems
• Solutions to Linear Systems

• Linear Combinations and Span
• Linear Independence
• The Rank of a Matrix
• A Basis for a Vector Space
• Projection onto a Subspace
• Row Space and Column Space of a Matrix
• Subspaces ofRⁿ
• The Nullspace of a Matrix
• The Rank Plus Nullity Theorem
• More Vector Spaces; Isomorphism

• Cramer's Rule
• The Classical Adjoint of a Square Matrix
• Definitions of the Determinant
• Laplace Expansions for the Determinant

• Determining the Eigenvalues of a Matrix
• Determining the Eigenvectors of a Matrix
• Eigenspaces
• Diagonalization
• Eigenvalue and Eigenvector Defined