Module 2: Matrix Algebra
Master the arithmetic of matrices: addition, multiplication, transposition, inverses, and factorizations.
Learning Objectives
By the end of this module, you will be able to:
- Perform matrix addition, scalar multiplication, and matrix multiplication
- Apply properties of matrix arithmetic (associativity, distributivity, non-commutativity)
- Compute the transpose of a matrix and use its properties
- Find the inverse of a matrix using row reduction
- Understand elementary matrices and their role in LU factorization
Module Lessons
1
Matrix Addition, Scalar Multiplication, Matrix Multiplication
Learn the fundamental operations on matrices, including the row-column rule for matrix multiplication.
35-45 minutes
2
Properties of Matrix Arithmetic and Transpose
Explore associativity, distributivity, and the surprising fact that matrix multiplication is NOT commutative. Learn the transpose operation.
30-40 minutes
3
The Inverse of a Matrix
Discover what it means for a matrix to be invertible, how to compute inverses via row reduction, and properties of inverse matrices.
35-45 minutes
4
Elementary Matrices and LU Factorization
Understand how row operations correspond to matrix multiplication, and factor a matrix as a product of lower and upper triangular matrices.
35-45 minutes