Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Systems and Matrices
Subtopic: Matrix Algebra

Overview

Today we delve into the algebra of matrices. Everything you learned to do with numbers in arithmetic such as multiplying or reciprocating you get to learn to do with matrices. Practice working the problems algebraically and electronically. See the class calendar for links to my Calculator Guide to Matrix Algebra and Calculator Guide to Determinants.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 5.4.1 Understand and properly use terminology and notation related to matrices and determinants
• 5.4.2 Find a specific element of a matrix of form amn
• 5.4.3 Find the order of a matrix
• 5.4.4 Recognize square and non-square matrices
• 5.4.5 Find the transpose of a matrix
• 5.4.6 Solve a matrix equation using the matrix equality rule
• 5.4.7 Find the determinant of a 2x2 or 3x3 matrix using the shortcut method
• 5.4.8 Find the determinant of a 4x4 or larger matrix electronically
• 5.4.9 Recognize if two matrices can be added or not based on their dimensions
• 5.4.10 Perform matrix addition, matrix subtraction, and scalar multiplication
• 5.4.11 Write a zero matrix of given size
• 5.4.12 Recognize an additive identity matrix and an additive inverse matrix
• 5.4.13 Recognize if two matrices can be multiplied or not based on their dimensions
• 5.4.14 Perform matrix multiplication
• 5.4.15 Know if matrix addition/multiplication is associative/commutative

Terminology

Terms you should be able to define: matrix, row, column, element, order, size, dimension, square matrix, non-square matrix, transpose, matrix equality rule, determinant, matrix addition, matrix subtraction, zero matrix, additive identity matrix, additive inverse matrix, scalar, scalar multiplication, matrix multiplication, associative property of matrices, commutative property of matrices

Text Notes

You can SKIP the "adjunct method" of finding a determinant and SKIP Cramer's Rule, if your text covers either.

Note that to o find a determinant of a:

• 2x2 matrix - use the shortcut method.
• 3x3 matrix - use the shortcut method shown in class.
• 4x4 matrices and larger - use a calculator! Take advantage of technology instead of the antiquated adjunct method.

rev. 2020-11-29