Identity and Inverse Matrices, Algebra 2

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Carleen Eaton

Grant Fraser

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Identity and Inverse Matrices

The identity matrix plays the role of the identity under multiplication.
The inverse of a matrix represents the inverse under multiplication.
A square matrix has an inverse if and only if its determinant is not zero.
The inverse of a 2 x 2 determinant can be calculated using a specific formula.

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Table of Contents

I. Equations and Inequalities
	Expressions and Formulas	28:56
	Properties of Real Numbers	23:45
	Solving Equations	24:41
	Solving Absolute Value Equations	17:36
	Solving Inequalities	19:27
	Solving Compound and Absolute Value Inequalities	24:08
II. Linear Relations and Functions
	Relations and Functions	38:15
	Linear Equations	12:50
	Slope	20:07
	Writing Linear Functions	27:36
	Special Functions	24:28
	Graphing Inequalities	30:37
III. Systems of Equations and Inequalities
	Solving Systems of Equations by Graphing	21:27
	Solving Systems of Equations Algebraically	31:26
	Solving Systems of Inequalities by Graphing	20:43
	Solving Systems of Equations in 3 Variables	21:27
IV. Matrices
	Basic Matrix Concepts	14:08
	Matrix Operations	16:40
	Matrix Multiplication	22:47
	Determinants	25:47
	Cramer's Rule	25:42
	Identity and Inverse Matrices	27:01
	Solving Systems of Equations with Matrices	28:40
V. Quadratic Functions and Inequalities
	Graphing Quadratic Equations	26:36
	Solving Quadratic Equations by Graphing	19:26
	Solving Quadratic Equations by Factoring	17:46
	Imaginary and Complex Numbers	37:41
	Completing the Square	16:42
	Quadratic Formula and the Discriminant	17:44
	Analyzing the Graphs of Quadratic Functions	23:00
	Graphing and Solving Quadratic Inequalities	34:38
VI. Polynomial Functions
	Properties of Exponents	20:28
	Operations on Polynomials	16:13
	Dividing Polynomials	29:26
	Polynomial Functions	29:34
	Analyzing Graphs of Polynomials	34:36
	Solving Polynomial Equations	19:23
	Remainder and Factor Theorems	27:52
	Roots and Zeros	31:04
	Rational Zero Theorem	29:27
VII. Rational Equations and Inequalities
	Operations on Functions	35:12
	Inverse Functions and Relations	18:12
	Square Root Functions and Inequalities	26:24
	nth Roots	24:06
	Operations with Radical Expressions	34:38
	Rational Exponents	24:36
	Solving Radical Equations and Inequalities	38:46
VIII. Radical Expressions and Equations
	Multiplying and Dividing Rational Expressions	30:11
	Adding and Subtracting Rational Exprsesions	51:53
	Graphing Rational Functions	45:13
	Direct, Joint, and Inverse Variation	21:49
	Solving Rational Equations and Inequalities	53:21
IX. Exponential and Logarithmic Relations
	Exponential Functions	28:22
	Logarithms and Logarithmic Functions	36:31
	Properties of Logarithms	29:50
	Common Logarithms	27:10
	Base 'e' and Natural Logarithms	19:52
	Exponential Growth and Decay	28:10
X. Conic Sections
	Midpoint and Distance Formulas	29:35
	Parabolas	26:11
	Circles	17:33
	Ellipses	38:57
	Hyperbolas	37:59
	Conic Sections	23:10
	Solving Quadratic Systems	28:18
XI. Sequences and Series
	Arithmetic Sequences	27:44
	Arithmetic Series	29:12
	Geometric Sequences	24:52
	Geometric Series	27:02
	Infinite Geometric Series	24:01
	Recursion and Special Sequences	17:11
	Binomial Theorem	38:25
	Proof and Mathematical Induction	19:53

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Identity and Inverse Matrices

QuickNotes™

Identity and Inverse Matrices

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