# 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

### Determinant when row is added

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)

### Determinant after row operations

VIDEO
10:25 minutes

What happens to the determinant when we perform a row operation

### 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