How do you find the determinant of #((2, 5, -3, -1), (3, 0, 1, -3), (-4, 5, -7, 8), (4, 10, -4, 1))#?

1 Answer
Apr 30, 2016

Answer:

#180#

Explanation:

#[[color(teal)(2),color(teal)(5),color(teal)(-3),color(teal)(-1)],[3,0,1,-3],[color(magenta)(-4),color(magenta)(5),color(magenta)(-7),color(magenta)(8)],[color(turquoise)(4),color(turquois)(10),color(turquoise)(-4),color(turquoise)(1)]]=#
#-># row3 #-# row1 #-># row3
#-># row4 #-2*# row1 #-># row4

#=[[color(orange)(2),color(blue)(5),-3,-1],[color(orange)(3),color(blue)(0),1,-3],[color(orange)(-6),color(blue)(0),-4,9],[color(orange)(0),color(blue)(0),2,3]]#
#-># changing column1 with colum2

#=-[[color(blue)(5),2,-3,-1],[0,3,1,-3],[0,-6,-4,9],[0,0,2,3]]#

#=-5.(-1)^(1+1)*[[color(violet)(3),1,color(crimson)(-3)],[color(violet)(-6),-4,color(crimson)(9)],[color(violet)(0),2,color(crimson)(3)]]#

#=-5*3*3*[[1,1,-1],[-2,-4,3],[0,2,1]]#

#=-45*[cancel(-4)+cancel(4)-(6-2)]=-45*[-4]=180#