This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.
This 17-minute video lesson looks at the determinant when one matrix has a row that is the sum of the rows of other matrices (and every other term is identical in the 3 matrices).
This 22-minute video lesson realizes that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix.
This 20-minute video lesson shows how to view the determinant of the transformation matrix as a scaling factor of regions.
This video shows an example using orthogonal change-of-basis matrix to find transformation matrix
This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.
This 12-minute video lesson looks at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other.