Unit Plan
CK-12 Foundation

Ck 12: Algebra: Limitations of Matrix Multiplication

For Students 10th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] This lesson shows you how to determine if two matrices can be multiplied together and explains that the commutative property does not apply.
PPT
Sophia Learning

Sophia: Using Determinants to Classify 3x3 Matrices: Lesson 2

For Students 9th - 10th Standards
This lesson demonstrates how the determinant of a 3x3 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Unit Plan
Sophia Learning

Sophia: Using Determinants to Classify 3x3 Matrices: Lesson 3

For Students 9th - 10th Standards
This lesson demonstrates how the determinant of a 3x3 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
PPT
Sophia Learning

Sophia: Using Determinants to Classify 2x2 Matrices: Lesson 2

For Students 9th - 10th Standards
This lesson demonstrates how the determinant of a 2x2 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Activity
Math Medics

S.o.s. Math: Application of Determinant to Systems: Cramer's Rule

For Students 9th - 10th
This lesson explains how the determinant is used for Cramer's Rule.
Handout
Math Notes and Math Tests

Pre Calculus Notes: The Inverse of a Square Matrix [Pdf]

For Students 9th - 10th Standards
Students explore the inverse of a square matrix. Topics examined are the inverse of a real number, using inverses to solve systems, and the determinant of a 2 x 2 matrix. Class notes and examples are included.
Handout
Wolfram Research

Wolfram Math World: Determinant Expansion by Minors

For Students 9th - 10th
This MathWorld site explains the technique for finding the determinant using minors. The site also suggests to use this method only on small matrices, giving a link to Guassian elimination for the alternative(larger matrices.) The site...
Activity
Varsity Tutors

Varsity Tutors: Hotmath: Practice Problems: Cramer's Rule and Determinant of a Matrix

For Students 9th - 10th Standards
Sixteen problems present a variety of practice using Cramer's Rule to solve equations and systems of equations and working with the determinant of a matrix. They are given with each step to the solution cleverly revealed one at a time....
Unit Plan
CK-12 Foundation

Ck 12: Algebra: Determining the Type of Linear System

For Students 9th - 10th
[Free Registration/Login may be required to access all resource tools.] Solve a system and use the result as a guide to identify its type.
Handout
Math Notes and Math Tests

Pre Calculus Notes: The Determinant of a Square Matrix [Pdf]

For Students 9th - 10th Standards
The resource investigates the determinant of a square matrix. Topics examined are computing determinants, Sarrus?s rule, and the cross product of two vectors. Class notes and examples are included.
Unit Plan
University of St. Andrews (UK)

University of St. Andrews: Matrices and Determinants

For Students 9th - 10th Standards
This resource explains determinants as related to mathematics and the history of determinants.
Activity
Interactive Mathematics

Interactive Mathematics: Finding the Inverse of a Matrix

For Students 9th - 10th Standards
Two methods are demonstrated for finding the inverse of a matrix. The examples are detailed and easy to follow. Several interactive examples are also provided.
Activity
Interactive Mathematics

Interactive Mathematics: Determinants

For Students 9th - 10th
Using determinants and Cramer's Rule, systems of two and three variables are solved step by step. Several examples are presented to demonstrate how Cramer's Rule is used.
Handout
Oak Ridge National Laboratory

Ornl: 7 Gaussian Elimination on Band Matrices

For Students 9th - 10th Standards
This site gives an example of solving a system of equations with the use of Gaussian Elimination.
Interactive
Other

Meta Calculator: Matrix Calculator

For Students 9th - 10th
Use this web-based matrix calculator to solve for functions and operations.
PPT
Sophia Learning

Sophia: Singular and Non Singular Matrices: Lesson 1

For Students 9th - 10th
This lesson introduces the notion of a singular matrix and provides a shortcut to determine whether or not a given 2x2 matrix is singular. It is 1 of 5 in the series titled "Singular and Non-Singular Matrices."
PPT
Sophia Learning

Sophia: Singular and Non Singular Matrices: Lesson 3

For Students 9th - 10th
This lesson introduces the notion of a singular matrix and provides a shortcut to determine whether or not a given 2x2 matrix is singular. It is 3 of 5 in the series titled "Singular and Non-Singular Matrices."
Handout
Purple Math

Purplemath: Minors and Cofactors: Expanding Along a Row

For Students 9th - 10th Standards
A "minor" is the determinant of the square matrix formed by deleting one row and one column from some larger square matrix. To find the determinant of the matrix A, you have to pick a row or a column of the matrix, find all the cofactors...
Handout
Wolfram Research

Wolfram Math World: Minor

For Students 9th - 10th
This site explains what a minor is relative to matrix manipulations and gives insight on how to use the program "Mathmatica" involving minors.
Activity
Ministry of Education and Universities of the Region of Murcia (Spain)

Ministerio De Educacion Y Ciencia: Geometria De Los Determinantes

For Students 9th - 10th Standards
In Spanish. In this interactive session you will study the second order determinant and its properties. Both methods geometrically and algebraically are presented.
Handout
University of St. Andrews (UK)

University of St. Andrews: Gottfried Wilhelm Von Leibniz

For Students 9th - 10th
This site from the University of St. Andrews provides a biographical account of the life of Gottfried Wilhelm von Leibniz. Includes links to mathematics topics such as matrices and determinants, quadratic, cubic and quartic equations, etc.
Activity
Texas Instruments

Texas Instruments: Polynomial Functions

For Teachers 9th - 10th Standards
In this set of questions, students will find the x-intercepts of a polynomial function, factor a polynomial, and determine the number of solutions of a polynomial equation. Questions are multiple choice and true/false; solutions are...
Unit Plan
CK-12 Foundation

Ck 12: Algebra: Consistent and Inconsistent Linear Systems

For Students 9th - 10th
[Free Registration/Login may be required to access all resource tools.] Identify a system as inconsistent, consistent, or dependent and determine how many solutions a system has.
Activity
University of Georgia

University of Georgia: Slope of Lines

For Teachers 9th - 10th Standards
This site provides a detailed unit on finding the slope of lines that investigates methods for solving systems of equations. Good lesson plan for class.

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