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

Answer:

#-47#

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#