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More determinant depth
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.
The determinant when a row is multiplied by a scalar
Correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant
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 of a matrix with duplicate rows
What happens to the determinant when we perform a row operation
The determinant of an upper triangular matrix
Calculating a 4x4 determinant by putting in in upper triangular form first.
Realizing that the determinant of a 2x2 matrix is equal to the area of the parallelogram defined by the column vectors of the matrix
Viewing the determinant of the transformation matrix as a scaling factor of regions