Chapter 1

Section 1.1

  • Examples: Solving Systems of Linear Equations with 3 Equations and 3 Variables

Section 1.2

  • Examples: Pivot Rows and Columns of a Matrix, Leading vs Free Variables

  • Examples: Solving Systems Using the Gauss-Jordan Method and Gaussian Method

Section 1.3

  • Lesson: Properties of Matrices: Equality, Addition, Subtraction, and Scalar Multiplication

  • Lesson: Matrix Multiplication

  • Examples: Matrix Addition, Subtraction and Scalar Multiplication

  • Examples: Matrix Multiplication

  • Examples: Matrix Operations with Transposes and Traces

  • Examples: Finding Values of k that Satisfy a Matrix Equations

Section 1.4

  • Examples: Simplifying a Matrix Expression Using Properties of Inverses

Section 1.5

  • Examples: Expressing a Matrix and its Inverse as the Product of Elementary Matrices

Section 1.7

  • Examples: Finding Values that Will Make a Matrix Symmetric

Section 1.8

  • Lesson: Intro to Linear Transformations

  • Lesson: Properties of Linear Transformations

  • Examples: Matrix Multiplication and Reflections

  • Examples: Matrix Multiplication and Orthogonal Projections

  • Examples: Matrix Multiplication and Rotations