Khan Academy: Linear Algebra: Showing That Inverses Are Linear

A video lesson proving that the product of a matrix and its transpose is invertible if all of the columns of the originial matrix are linearly independent. [12:34]

Video first reviews how to find the basis for the column space of a matrix using the reduced row echelon form. Proves that the basis for the column space using the reduced row echelon form method spans the column space. Uses this and the...

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 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 a function is. Explains what the identity function is and uses it to define what makes a function invertible. Shows that the inverse will be unique. This video also appears in the strand Algebra: Functions. [18:53]

An instructional video that explains how the method for finding the inverse transformation matrix is derived. It is the same method for finding the inverse for any invertible matrix. [18:00]

Video shows how to determine the inverse of a 3 by 3 matrix using the Gauss-Jordan elimination method. This video also appears in the strand Algebra: Matrices. [13:35]

A video lesson in which a formula is derived for finding the inverse of a 2 x 2 matrix. Addresses that a 2 x 2 matrix is only invertible if the determinant is not equal to 0. Defines the determinant and shows two examples of calculating...

A video lesson that works through a concrete example to find the inverse of a 3 x 3 matrix. The original matrix is augmented by the identity matrix and then put in reduced row echelon form. The result of the row operations on the...

Video example of finding the inverse of a 3 by 3 matrix. Includes using expansion by minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix. This video also appears in the strand Algebra:...