How do you find the determinant of ((3, 4, 5, 2), (1, 0, 1, 0), (, 2, 3, 6, 3), (, 7, 2, 9, 4))?

1 Answer
May 3, 2016

-24

Explanation:

((color(teal)(3),4,color(magenta)(5),2),(color(teal)(1),0,color(magenta)(1),0),(color(teal)(2),3,color(magenta)(6),3),(color(teal)(7),2,color(magenta)(9),4))=
-> column3 - column1 -> column3

=((color(gold)(3),4,2,2),(color(blue)(1),color(gold)(0),color(gold)(0),color(gold)(0)),(color(gold)(2),3,4,3),(color(gold)(7),2,2,4))

=1*(-1)^(2+1)*((4,2,2),(3,4,3),(2,2,4))
=-[64+12+12-(16+24+24)]
=-88+64=-24