This 16-minute video lesson shows that a projection onto a subspace is a linear transformation. [Linear Algebra playlist: Lesson 110 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 25-minute video lesson introduces the idea of an angle between two vectors.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 19-minute video lesson provides dot and cross product comparison and Intuition.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 27-minute video lesson provides an example using the orthogonal change-of-basis matrix to find the transformation matrix. [Linear Algebra playlist: Lesson 128 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 18-minute video lesson shows how to solve a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 30 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 9-minute video lesson provides definitions of the vector dot product and vector length.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This 19-minute video lesson proves the triangle inequality for vectors in Rn.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.