A=(13 11 9 12, 11 6 3 10, 17 8 10 9, 33 6 1 2)，calculate det

To calculate the determinant of a 4x4 matrix, we can use the method of cofactors.

The matrix A is:

A = [13 11 9 12] [11 6 3 10] [17 8 10 9] [33 6 1 2]

The determinant of a 4x4 matrix can be calculated as follows:

det(A) = a11(C11) - a12(C12) + a13(C13) - a14(C14)

where aij is the element in the i-th row and j-th column, and Cij is the cofactor of aij.

The cofactor Cij is given by (-1)^(i+j) times the determinant of the 3x3 matrix that remains after removing the i-th row and j-th column.

So, we need to calculate the four 3x3 determinants:

C11 = det([6 3 10, 8 10 9, 6 1 2]) = 6*(102 - 91) - 3*(82 - 96) + 10*(81 - 106)

C12 = det([11 3 10, 17 10 9, 33 1 2]) = 11*(102 - 91) - 3*(172 - 933) + 10*(171 - 1033)

C13 = det([11 6 10, 17 8 9, 33 6 2]) = 11*(82 - 96) - 6*(172 - 933) + 10*(176 - 833)

C14 = det([11 6 3, 17 8 10, 33 6 1]) = 11*(81 - 106) - 6*(171 - 1033) + 3*(176 - 833)

Then, substitute C11, C12, C13, C14 back into the formula for det(A):

det(A) = 13C11 - 11C12 + 9C13 - 12C14

This will give you the determinant of the matrix A.

This process involves a lot of calculations, so it's recommended to use a calculator or software that can handle matrix operations.