Math 115

Professor: Faisal Al-Faisal

Linear Algebra course at the University of Waterloo

Linear Algebra is the study of vectors and vector spaces.

Chapter 1 §

• Properties of Vector Algebra
• The Norm and Dot Product
• Vector Equations of Lines and Planes
• Cross Product
• Scalar Equations of Planes
• Projection

Chapter 2 §

• Systems of Linear Equations
• Rank
• Homogeneous System of Linear Equations
• Elementary Row Operations

Chapter 3 §

• Matrices
• Matrix-Vector Product
• The Matrix Equation
• Matrix Inverse

Chapter 4 §

• Spanning Sets
• Subspaces of R
• Bases and Dimensions
• Fundamental Subspaces Associated with a Matrix

Chapter 5 §

• Linear Transformations
• Examples of Linear Transformations
• The Kernel and the Range

Chapter 6 §

• Determinant

Chapter 7 §

• Polar Form

Chapter 8 §

• Eigenvalues and Eigenvectors
• Eigenspaces
• Diagonalization

Midterm §

• Math 115 - Midterm Prep

Final §

• Math 115 - Final Prep