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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

18. Systems of Equations and Matrices

Introduction to Matrices

18. Systems of Equations and Matrices

Introduction to Matrices: Videos & Practice Problems

Video Lessons Practice Worksheet

18 problems

Problem 1Multiple Choice

Find the given matrices (if possible):
a. PQ
b. QP
Matrices P and Q for the introduction to matrices in college algebra.

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Problem 2Multiple Choice

Express the following expression in its partial fraction decomposition.

(6y² - 3y + 45)/[(y - 5)(y² + 3y + 5)]

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Problem 3Multiple Choice

Determine the system of linear equations associated to the following augmented matrix. Use the variables x, y, and z.

Augmented matrix representing a system of linear equations for x, y, z.

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Problem 4Multiple Choice

Determine the augmented matrix that corresponds to the system of equations shown:

System of equations for college algebra, chapter 7, introduction to matrices.

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Problem 5Multiple Choice

Perform the following matrix operation: A - B

Matrix A with elements 5, -6, 2 and Matrix B with elements -7, 0, -3.

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Problem 6Multiple Choice

Consider the following matrices:

Matrix A and B for the equation X + A = B in college algebra.

Solve the following matrix equation for X: X + A = B

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Problem 7Multiple Choice

Perform the following matrix operation: - 3A

Matrix A with elements 7, 1, 6, 5, 4, 8.

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Problem 8Multiple Choice

Perform the following matrix operation: A - B

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Problem 9Multiple Choice

Rewrite the following expression in the partial fraction decomposition form. Do not solve for the constants!

(8y + 9)/(y + 3)(y - 5)²

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Problem 10Multiple Choice

What are the dimensions of a matrix with 4 rows and 5 columns?

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Problem 11Multiple Choice

Convert the system of equations 3x + 2y = 5 and 4x - y = 6 into an augmented matrix.

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Problem 12Multiple Choice

Given the matrix [[1, 2, 3], [4, 5, 6]], perform the row operation of swapping the two rows.

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Problem 13Multiple Choice

Using Gaussian elimination, solve the system represented by the matrix [[1, 2, 3], [0, 1, 4]]. What is the value of y?

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Problem 14Multiple Choice

What is the main difference between Gaussian elimination and Gauss-Jordan elimination?

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Problem 15Multiple Choice

Why are matrices used to represent systems of equations?

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Problem 16Multiple Choice

When converting the system of equations 2x + 3y = 5 and x - y = 2 into a matrix, why is it important to align the variables consistently?

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Problem 17Multiple Choice

Why are zeros significant in matrix operations?

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Problem 18Multiple Choice

Perform the row operation of adding twice the first row to the second row for the matrix [[1, 2, 3], [4, 5, 6]]. What is the new second row?

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Two Variable Systems of Linear Equations Practice Problems Determinants and Cramer's Rule Practice Problems

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Introduction to Matrices: Videos & Practice Problems

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System of Linear Equations Calculator

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Gauss-Jordan Elimination Calculator

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