How do you find the determinant of ((2, 0, -1, 3), (-1, 1, 0, 2), (0, 3, 2, 4), (4, 1, -1, 0))?
1 Answer
May 2, 2016
Explanation:
[[color(teal)(2),0,-1,color(orange)(3)],[color(teal)(-1),1,0,color(orange)(2)],[color(teal)(0),3,2,color(orange)(4)],[color(teal)(4),1,-1,color(orange)(0)]]=
-> column4+2* column1-> column4=
[[color(teal)(2),color(orange)(0),-1,7],[color(teal)(-1),color(orange)(1),0,0],[color(teal)(0),color(orange)(3),2,4],[color(teal)(4),color(orange)(1),-1,8]]
-> column1+ column2-> column1
=[[2,color(gold)(0),-1,7],[color(gold)(0),color(blue)(1),color(gold)(0),color(gold)(0)],[3,color(gold)(3),2,4],[5,color(gold)(1),-1,8]]
=1*(-1)^(2+2)[[2,-1,7],[3,2,4],[5,-1,8]]
=32-20-21-(70-8-24)=-9-38=-47