Khan Academy: Linear Algebra: Matrices to Solve a Vector Combination Problem

Sal dissects basic algebraic equations of the form Ax=B. He encourages viewers to fully understand the equations before learning how to manipulate them. Furthermore, he teaches students how to solve the equations systematically. The...

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 explains why a matrix is singular if its determinant is 0. Illustrates that when a matrix equation is built with a singular matrix, then there are no solutions because the system it represents is that of two parallel lines. Shows...

Video first reviews what the null space is and how to solve for it using reduced row echelon form. Shows that any solution to the inhomogeneous system Ax = b will be the sum of a particular solution and a homogeneous solution. Extends...

Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations. Relates vector transformations to video game graphics. This video...

Video first shows that matrix vector multiplication is another way to represent a transformation and then shows that matrix vector products are linear transformations. Relates vector transformations to video game graphics. This video...

Video shows example of multiplying matrices. Includes explanation of the dimensions needed in order for matrices to be able to be multiplied. Connects to the composition of linear transformations. This video also appears in the strand...

Video first explains and gives examples of identity matrices. Then explains what an inverse matrix is and shows how to calculate the inverse of a 2x2 matrix. [14:14]

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 first reviews the criteria for a subspace and then goes through the steps to show the null space meets the criteria and is a a subspace. This video also appears in the strand Algebra: Matrices. [10:21]