Calculating the Determinant of a 4x4 Matrix

[andrey21]

Find the determinant of the following 4x4 matrix

-1 0 0 0
-15 7 -15 5
-5 1 -6 1
6 -7 6 -5



Here is my attempt

Ive seen that I should do the following:

-1.(determinant of 3x3 matrix)-0.(determinant of 3x3 matrix) + 0.(determinant of 3x3 matrix)-0.(determinant of 3x3 matrix)

which would simplify to

-1.(determinat of 3x3 matrix)

IS THIS CORRECT??

 

[Mark44]

Find the determinant of the following 4x4 matrix

-1 0 0 0
-15 7 -15 5
-5 1 -6 1
6 -7 6 -5



Here is my attempt

Ive seen that I should do the following:

-1.(determinant of 3x3 matrix)-0.(determinant of 3x3 matrix) + 0.(determinant of 3x3 matrix)-0.(determinant of 3x3 matrix)

which would simplify to

-1.(determinat of 3x3 matrix)

IS THIS CORRECT??

Yes. To be more specific, it is -1 times the determinant of this submatrix:

7 -15 5
1 -6 1
-7 6 -5

I.e., the cofactor of the -1 entry in row 1, column 1.

 

[andrey21]

Great thanks mark 44 I ended up with the correct answer of -18:)