Interactive
CK-12 Foundation

#### Cramer's Rule

For Students 10th - 12th Standards
Use matrices to solve systems of equations. The interactive introduces Cramer's Rule, using determinants of matrices to solve systems of equations. Color coding helps pupils place entries correctly from the system.
Instructional Video5:51
Krista King Math

#### Solving Systems of Equations with Cramer's Rule

For Students 9th - 12th Standards
Show how matrices can be helpful for solving systems of equations. The video illustrates an example of solving a two-variable system utilizing Cramer's Rule. The instructor shows how to find the determinant of each matrix and then uses...
Lesson Plan
Curated OER

#### Cramer's Rule ID: 8793

For Teachers 9th - 12th Standards
Mathematicians are introduced to Cramer’s Rule and use it to solve three systems that have one solution, no solutions, and an infinite number of solutions.  Students use TI-Nspire to graph the systems to verify their answers and...
Worksheet
Curated OER

#### Solving Systems of Three Equations with Cramer's Rule

For Students 10th - 12th
In this systems of equations worksheet, students solve systems of equations using Cramer's Rule. This four-page worksheet contains 16 problems. Answers are provided on the last two pages.
Worksheet
Curated OER

#### Solving Systems of Two Equations with Cramer's Rule

For Students 9th - 11th
In this systems of equations learning exercise, students use Cramer's Rule to solve a systems of equations learning exercise. This two-page learning exercise contains 14 problems. Answers are provided on the last page.
Worksheet
Curated OER

#### Topic 3.3: Cramer's Rule

For Students 10th - 12th
In this Cramer's Rule activity, learners use Cramer's Rule to solve system of equations. They identify the value of each given determinant. This one-page activity contains ten multi-step problems.
Worksheet
Curated OER

#### Chapter 3.3 - Cramer's Rule

For Students 8th - 10th
In this Cramer's rule worksheet, students solve 4 problems in which they find the determinant. They then solve 8 more problems in which they use Cramer's Rule to solve each system of equations.
Worksheet
Curated OER

#### Cramer's Rule

For Students 11th - 12th
In this Cramer's Rule worksheet, learners solve and complete 18 different problems related to trigonometry. First, they solve each system of equations using Cramer's Rule. Then, students solve using matrix elimination. Finally, they...
Worksheet
Curated OER

#### Cramer's Rule

For Students 11th - Higher Ed
In this Cramer's Rule activity, students first evaluate five determinants or square matrix. Then they solve the last five problems by applying Cramer's Rule. Students identify and define Cramer's Rule as a theorem used with linear...
Worksheet
Curated OER

#### Equations and Inequalities

For Students 11th
In this equations and inequalities review worksheet, 11th graders solve and complete 100 various types of problems. First, they solve each equation using the quadratic formula or completing the square. Then, students solve using matrices...
Worksheet
Curated OER

#### Cramer's Rule

For Students 9th - 11th
In this algebra worksheet, students solve problems with matrices. They add, subtract and multiply matrices. There are 7 questions.
Worksheet
Curated OER

#### Systems of Equations

For Students 10th
In this systems of equations activity, 10th graders solve and complete 4 different sets of problems. First, they state the domain for each equation. Then, students solve each system of equations using Cramer's Rule. They also find the...
Worksheet
Curated OER

#### Linear Systems: Applications of Determinants

For Students 12th - Higher Ed
For this determinant worksheet, students explore determinants, area and volume. This two-page worksheet contains explanations and examples. It provides two problems for students to solve.
Worksheet
Curated OER

#### Linear Systems: Applications of Determinants

For Students Higher Ed
In this determinant worksheet, students use determinants to find area and volume. This two-page worksheet contains examples, explanations and four problems.
Worksheet
Curated OER

#### Solving Linear Systems Using Matrices

For Students 9th - 12th Standards
Start with the definition of a determinant and how to evaluate a 2x2 determinant. Apply this skill to solve systems of two equations with two unknowns by using Cramer's rule. These four basic problems would be good for a quick review or...
eBook
Rice University

#### College Algebra

For Students 9th - Higher Ed Standards
Is there more to college algebra than this? Even though the eBook is designed for a college algebra course, there are several topics that align to Algebra II or Pre-calculus courses. Topics begin with linear equation and inequalities,...
eBook
Rice University

#### Precalculus

For Students 11th - Higher Ed Standards
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
Lesson Plan
Curated OER

#### Second Order Determinants

For Teachers 9th - 12th
Students solve linear equations using Cramer's Rule. In this algebra lesson, students use second order determinants to solve equations with two unknowns using a t-chart and identifying solution set.
Worksheet
Curated OER

#### Final Exam Review: College Algebra

For Students 11th - Higher Ed
In this final exam review worksheet,s students solve systems of equations, polynomials and factor quadratic equations.  They identify the slope of a line and write linear equations.  Students use Cramer's rule, graphing, substitution,...
Instructional Video9:59
1
1
3Blue1Brown

#### Linear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2

For Students 11th - Higher Ed Standards
What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...
Instructional Video14:12
1
1
3Blue1Brown

#### Dot Products and Duality | Essence of Linear Algebra, Chapter 7

For Students 11th - Higher Ed Standards
The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...
Instructional Video12:09
1
1
3Blue1Brown

#### Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6

For Students 11th - Higher Ed Standards
Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse matrix to...
Instructional Video10:03
1
1
3Blue1Brown

#### The Determinant | Essence of Linear Algebra, Chapter 5

For Students 11th - Higher Ed Standards
Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...
Instructional Video10:04
1
1
3Blue1Brown

#### Matrix Multiplication as Composition | Essence of Linear Algebra, Chapter 4

For Students 11th - Higher Ed Standards
Take a different view at matrix multiplication. Based on vector transformations, the video presents matrix multiplication as the result of the composition of multiple linear transformations. The presentation explains the numerical...