More determinant depth

9 videos
In the last tutorial on matrix inverses, we first defined what a determinant is and gave several examples of computing them. In this tutorial we go deeper. We will explore what happens to the determinant under several circumstances and conceptualize it in several ways.

Determinant when row multiplied by scalar

VIDEO 13:20 minutes
The determinant when a row is multiplied by a scalar

(correction) scalar multiplication of row

VIDEO 2:52 minutes
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 16:55 minutes
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)

Duplicate row determinant

VIDEO 8:19 minutes
Determinant of a matrix with duplicate rows

Determinant after row operations

VIDEO 10:25 minutes
What happens to the determinant when we perform a row operation

Upper triangular determinant

VIDEO 8:07 minutes
The determinant of an upper triangular matrix

Simpler 4x4 determinant

VIDEO 9:13 minutes
Calculating a 4x4 determinant by putting in in upper triangular form first.

Determinant and area of a parallelogram

VIDEO 21:37 minutes
Realizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix

Determinant as scaling factor

VIDEO 20:09 minutes
Viewing the determinant of the transformation matrix as a scaling factor of regions