Linear Algebra

Module II

Materials go up as we reach each lecture. See the Schedule for dates and assessments.

Practice problems for this module, collected: Problems (PDF) Solutions (PDF)

Module notes covering this whole module: Linear Algebra Notes

Lecture 3: Matrices and Matrix Operations

Topics: Matrices; addition, subtraction, scalar and matrix multiplication

Textbook references: 4.1, 4.2

Slides Slides (PDF) Worksheet: Matrix Operations Practice problems

Lecture 4: Matrix Multiplication, Vectors, and Special Matrices

Topics: Matrix multiplication; vectors; linear dependence; identity, null, idempotent, and transpose matrices

Textbook references: 4.2–4.6

Slides Slides (PDF) Practice problems

Lecture 5: Inverse of a Matrix

Topics: Inverse of a matrix; conditions for nonsingularity

Textbook references: 4.6, 5.1

Slides Slides (PDF)

Lecture 6: The Determinant and the Inverse

Topics: Computing the determinant and the inverse

Textbook references: 5.2–5.4

Slides Slides (PDF) Worksheet: Determinant and Inverse Practice problems Video: Finding the Inverse Video: Worked Example

Lecture 7: Solving Systems of Linear Equations

Topics: Solving systems of linear equations by matrix inversion and Cramer’s rule; applications

Textbook references: 5.4, 5.5, 4.7

Slides Slides (PDF) Worksheet: Solving Systems of Equations Practice problems