Khan Academy: Linear Algebra:defining a Plane in R3 With Point and Normal Vector

Video shows how to define a plane in R3 using a point on the plane and a normal vector to the plane. Includes a visual representation to help understanding. [13:53]

Video demonstrating that the area of a parallelogram created by graphing the column vectors of a 2x2 matrix is the equivalent to the absolute value of the determinant of the matrix. Pythagorean theorem, in conjunction with calculating a...

Video solving a IIT-JEE problem about the distances between two planes. Solution requires finding the equation of one of the planes by first finding points that lie on that plane, using those to find two vectors on the plane and then...

Video gives examples of vector addition, graphing vectors, multiplying vectors by a scalar and vector subtraction using vectors in R2 and extends to vectors in other dimensions. [25:33]

Video starts with reviewing matrix notation. Defines multiplying a matrix by a vector and shows examples. Shows how the matrix-vector products can be interpreted as the dot product of column vectors with a matrix or as a weighted linear...

Video first gives the conditions that define a linear transformation. Gives examples of determining if a transformation is linear or not. Shows several types of notation for vector transformations. [13:52]

Demonstrates how to find the appropriate combination of two given vectors in order to obtain a third given vector. This is done by representing the problem with a single matrix equation and solving that equation. [14:20]

A more formal understanding of functions. This video introduces the term codomain and contrasts it with the term range. It also introduces the terminology scalar-valued function, real-valued function, and vector-valued function. [16:01]

This video shows the equation for a plane in R3 using a point on the plane and a normal vector.

Video uses the vector triangle inequality and the law of cosines to demonstrate and prove the definition of the angle between vectors. Uses the definition of the angle between vectors to define perpendicular vectors. Shows that the dot...