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Interactive
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\n\"Cramer's\n\n
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\nCK-12 Foundation\n
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\nCramer's Rule\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nUse 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.\n
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Instructional Video5:51
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\n\"Solving\n\n
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\nKrista King Math\n
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\nSolving Systems of Equations with Cramer's Rule\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nShow 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...\n
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Lesson Plan
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\n\"Cramer's\n\n
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\nCurated OER\n
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\nCramer's Rule ID: 8793\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nMathematicians 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.  High schoolers use TI-Nspire to graph the systems to verify their answers...\n
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Worksheet
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\n\"Solving\n\n
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\nCurated OER\n
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\nSolving Systems of Three Equations with Cramer's Rule\n

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\n\nFor Students\n\n10th - 12th\n
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\nFor 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.\n
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\n\"Solving\n\n
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\nCurated OER\n
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\nSolving Systems of Two Equations with Cramer's Rule\n

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\n\nFor Students\n\n9th - 11th\n
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\nIn this systems of equations worksheet, students use Cramer's Rule to solve a systems of equations worksheet. This two-page worksheet contains 14 problems. Answers are provided on the last page.\n
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\n\"Topic\n\n
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\nCurated OER\n
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\nTopic 3.3: Cramer's Rule\n

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\n\nFor Students\n\n10th - 12th\n
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\nIn this Cramer's Rule worksheet, learners use Cramer's Rule to solve system of equations. They identify the value of each given determinant. This one-page worksheet contains ten multi-step problems.\n
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\n\"Chapter\n\n
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\nCurated OER\n
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\nChapter 3.3 - Cramer's Rule\n

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\n\nFor Students\n\n8th - 10th\n
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\nIn 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.\n
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\n\"Cramer's\n\n
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\nCurated OER\n
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\nCramer's Rule\n

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\n\nFor Students\n\n11th - 12th\n
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\nFor this Cramer's Rule worksheet, students 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...\n
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\n\"Cramer's\n\n
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\nCurated OER\n
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\nCramer's Rule\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this Cramer's Rule worksheet, 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...\n
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\n\"Equations\n\n
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\nCurated OER\n
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\nEquations and Inequalities\n

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\n\nFor Students\n\n11th\n
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\nIn this equations and inequalities review activity, 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...\n
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\n\"Cramer's\n\n
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\nCramer's Rule\n

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\n\nFor Students\n\n9th - 11th\n
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\nIn this algebra worksheet, students solve problems with matrices. They add, subtract and multiply matrices. There are 7 questions.\n
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\n\"Systems\n\n
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\nCurated OER\n
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\nSystems of Equations\n

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\n\nFor Students\n\n10th\n
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\nIn 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...\n
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Worksheet
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\n\"Linear\n\n
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\nCurated OER\n
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\nLinear Systems: Applications of Determinants\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn 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. \n
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\n\"Linear\n\n
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\nLinear Systems: Applications of Determinants\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this determinant worksheet, students use determinants to find area and volume. This two-page worksheet contains examples, explanations and four problems.\n
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Worksheet
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\n\"Solving\n\n
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\nSolving Linear Systems Using Matrices\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nStart 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...\n
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eBook
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\n\"College\n\n
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\nRice University\n
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\nCollege Algebra\n

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\n\nFor Students\n\n9th - Higher Ed\n\nStandards\n
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\nIs 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,...\n
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eBook
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\n\"Precalculus\n\n
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\nRice University\n
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\nPrecalculus\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nTake 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...\n
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Worksheet
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\n\"Final\n\n
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\nFinal Exam Review: College Algebra\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn 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,...\n
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Instructional Video9:59
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\n\"Linear\n\n
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\nLinear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nWhat 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...\n
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Instructional Video14:12
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\n\"Dot\n\n
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\nDot Products and Duality | Essence of Linear Algebra, Chapter 7\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nThe 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...\n
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Instructional Video12:09
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\n\"Inverse\n\n
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\nInverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nDetermine 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...\n
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Instructional Video10:03
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\nThe Determinant | Essence of Linear Algebra, Chapter 5\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nDetermine 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...\n
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Instructional Video10:04
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\n\"Matrix\n\n
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\nMatrix Multiplication as Composition | Essence of Linear Algebra, Chapter 4\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nTake 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...\n
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Instructional Video10:59
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\n\"Linear\n\n
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\nLinear Transformations and Matrices | Essence of Linear Algebra, Chapter 3\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nAre all transformations of the plane linear transformations? The video provides examples of transformations of the plane and provides the definition of linear transformations. The resource begins the discussion of using matrix...\n
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