Khan Academy: More Determinant Depth: Determinant When Row Is Added

A video showing what happens to the determinant when we perform a row operation.

Correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant

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.

A video lesson proving that the determinant of an upper triangular matrix is the product of the all of the entries along the main diagonal

A video lesson proving that if a matrix has duplicate rows then its determinant will be 0.

This video, shows how to calculate a 4x4 determinant by putting in in upper triangular form first.

Sal dives in even deeper with a few more examples of exponential decay. Practice calculating k from half-life, and calculating initial mass. [7:21]

A video lesson describing how the determinants for larger matrices can be found using cofactor expansion on any row or column. Illustrates that it is helpful to choose rows or columns with zeros in order to simplify the computations....

Video reviews from previous videos that a function is invertible if and only if it is onto and one-to-one. Shows how to determine if a linear transformation is onto by showing that the columns of the transformation matrix span the...

A video lesson proving that any projection onto a subspace is actually a linear transformation. Also, if given the basis for the subspace then the specific transformation matrix for the projection can be found. Includes a brief...