Linear Systems: Geometric Interpretation of Eigenvalues
In this geometric interpretation worksheet, students prove the exponentiation of a matrix and the Eigenvalues of an inverse. This two-page worksheet contains explanations, examples, theorems and two problems for students to solve.
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Independent and Dependent Systems
Learners practice their linear algebra skills with laser focus on the unique cases of independent and dependent systems in this short problem set and presentation. The pairing of the two concepts really brings into focus the difference...
10th - 12th Math CCSS: Adaptable
Linear Systems: Geometric Interpretation of Eigenvalues and Eigenvectors
In this interpretation of eigenvalues and eigenvectors worksheet, students probe the given results of exponentiation of a matrix. They tell the implications of this result. Students prove that the eigenvectors of a symmetric matrix are...
Higher Ed Math
Systems of Equations and Inequalities
This is a comprehensive instructional activity on creating and solving equations and systems of equations and inequalities. Problems range from basic linear equations to more complex systems of equations and inequalities based on a...
8th - 12th Math CCSS: Adaptable
Solving General Systems of Linear Equations
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
11th - 12th Math CCSS: Designed
The Determinant | Essence of Linear Algebra, Chapter 5
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...
10 mins 11th - Higher Ed Math CCSS: Adaptable
Cross Products in the Light of Linear Transformations | Essence of Linear Algebra Chapter 8 Part 2
What do cross products and parallelpipeds have in common? The video discusses the geometric representation of the cross product. The geometric interpretation explains why the computational trick in calculating the cross product works.
13 mins 11th - Higher Ed Math CCSS: Adaptable
Eigenvectors and Eigenvalues | Essence of Linear Algebra, Chapter 10
Find vectors that stay on their spans after a linear transformation. The 14th video in the series of 15 introduces the concept of eigenvectors, vectors that are only scaled during a linear transformation. The presentation illustrates the...
17 mins 11th - Higher Ed Math CCSS: Adaptable
Essence of Linear Algebra Preview
Make connections with linear algebra. The video introduces the concept of linear algebra and its geometric underpinnings. The resource makes the case that a complete understanding of linear algebra topics should include geometric...
5 mins 11th - Higher Ed Math CCSS: Adaptable