Khan Academy: Linear Algebra: Upper Triangular Determinant

Video demonstrating how to find the determinant of a 4x4 matrix by using row operations and row replacements to get the matrix into upper triangular form. [9:13]

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...

A video lesson proving that if a matrix has duplicate rows then its determinant will be 0. It follows then that such a matrix will not be invertible. [8:19]

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]

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 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 first reviews the meaning of functions and talks about functions mapping sets from R^n to R^m. Gives examples of writing functions in vector notation. Explains that in linear algebra a transformation is just a function operation on...

An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...

Video demonstrating that the determinant of a matrix is equivalent to the determinant of the transpose of a matrix. Proof by induction is used to prove this property. [14:10]

Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram. Includes...