Step 4: Find the determinant of the above matrix. Step 5: Now replce the second column of matrix A by the answer matrix. Step 6: Find the determinant of the above matrix. Step 7: Now calculate the values of x 1 & x 2 by using formulas. For x1. x 1 = -0.0588. For x2. x 2 = 1.1176. Cramer's rule calculator solves a matrix of 2x2, 3x3, and 4x4 Unfortunately this is a mathematical coincidence. It is NOT the case that the determinant of a square matrix is just a sum and difference of all the products of the diagonals. For a 4x4 matrix, you expand across the first column by co-factors, then take the determinant of the resulting 3x3 matrices as above. This leaves me with a "mini matrix", if you will. The determinant of this is the minor of the first element. See that this is exactly what you're doing when you find a cross product, but there's more. What you're actually doing during a cross product is finding the cofactors. The cofactor of an element (symbolized as A) has a formula: The first step in computing the determinant of a 4×4 matrix is to make zero all the elements of a column except one using elementary row operations. We can perform elementary row operations thanks to the properties of determinants. In this case, the first column already has a zero. .

finding determinant of 4x4 matrix