SOLUTION: Compute the determinant: 4 0 -1 3 6 -2 -2 5 1 Complete lost on this one. Please help.

Algebra ->  Matrices-and-determiminant -> SOLUTION: Compute the determinant: 4 0 -1 3 6 -2 -2 5 1 Complete lost on this one. Please help.      Log On


   

Question 979883: Compute the determinant:
4 0 -1
3 6 -2
-2 5 1
Complete lost on this one. Please help.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!

Since the matrix contains zero in the first row,  I will use  cofactoring the determinant along the first row  (see the lesson  Co-factoring the determinant of a 3x3 matrix in this site):

det %28matrix%283%2C3%2C+4%2C0%2C-1%2C+3%2C6%2C-2%2C+-2%2C5%2C1%29%29 = 4*det%28matrix%282%2C2%2C+6%2C-2%2C+5%2C1%29%29 - 0*det%28matrix%282%2C2%2C+3%2C-2%2C+-2%2C1%29%29 + (-1)*det%28matrix%282%2C2%2C+3%2C6%2C+-2%2C5%29%29 =

                          = 4*det%28matrix%282%2C2%2C+6%2C-2%2C+5%2C1%29%29 + (-1)*det%28matrix%282%2C2%2C+3%2C6%2C+-2%2C5%29%29 = 4*(6*1 - 5*(-2)) - (3*5 - (-2)*6) = 4*(6 - (-10)) - (15 - (-12)) = 4*(6 + 10) - (15 + 12) = 4*16 - 27 = 64 - 27 = 37.