4x4 matrix determinant

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??

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Mark44
Mentor
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.

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