Determinant From Triangular Form

In this lesson, we will learn how to find the determinant of a 4 x 4 matrix (shortcut method) by converting the matrix into upper triangular form. When a matrix is in this form, we have a special property that tells us the determinant can be found as the product of the diagonal entries. There are a few things to keep in mind as we use this method. If we swap two rows, the sign of the determinant changes. This is true each time we swap rows, so we must keep track of the sign. Additionally, if we replace a row by the sum of that row and a nonzero constant multiple of some other row, there is no change to our determinant.