Evaluate the determinant of the matrix

[8. 3 -2]
[-1 3 2]
[ 5 -1 1]

Question

Evaluate the determinant of the matrix

[8.     3    -2]
[-1      3     2] 
[ 5     -1     1]

danjs · Answer

scalar triple product

anonymous · Answer

what?

usukidoll · Answer

cofactor expansion... that's needed to shrink the matrix down to a 2 x 2

danjs · Answer

A * (B x C)

anonymous · Answer

How?

danjs · Answer

do you know a 2 by 2 determinant?

anonymous · Answer

yes! i just don't know how to find the determinant for a 3x3 matrix

danjs · Answer

Determinant of 2 by 2 matrix   = a*d - cd
[a  b]
[c  d]

danjs · Answer

ok...

usukidoll · Answer

ad - bc for determinant of a 2 x 2 matrix
for a 3 x 3 matrix we have to use cofactor expansion.

anonymous · Answer

how do i do cofactor expansion?

danjs · Answer

|dw:1438052983671:dw|

usukidoll · Answer

Cofactor expansion
expanding a row ... find the minors and the cofactors of the first row entries ( you can choose second row or third row entries but the sign pattern is different).

danjs · Answer

|dw:1438053078307:dw|

danjs · Answer

Cover first column,   8*det of that 2x2 is the first of 3 terms

danjs · Answer

look up determinant of 3 x 3 matrix.. lol this is alot of drawing

usukidoll · Answer

the signs for the 3 x 3 matrix is like a checkerboard |dw:1438053171537:dw| that's why I use the first drawing a lot.