4x4 Determinant

To solve a determinant of order 4 or higher, one of the lines of the determinant should be formed by zeros, except one: the base element which will be worth 1 or −1.

Follow these steps:

1.If any element of the determinant is 1, choose one of the following lines: the row or column containing the 1. Keep in mind, that the line that contains the largest number of zero elements should be selected.

4x4 Determinant

2.If there is no 1 in the elements:

1.Look at the line containing the maximum number of zero elements and operate so that one of the elements of this line is 1 or −1 (operating with a parallel line).

Solving a 4x4 Determinant

2.Divide the line by one of its elements, then the determinant should be multiplied by that element so that its value does not vary.

Solving a 4x4 Determinant

3.Continue to operate until all the elements of the row or column where the basic element is located are zeros.

Solving a 4x4 Determinant

4.Take the cofactor of the basic element, so that a determinant of order one less than the original is obtained.

Determinant Solution = 2(-58)