How do you find the determinant of #((3, 1, -2, 1), (1, 1, -3, 2), (2, 0, 2, 3), (3, 3, 1, -3)) # ?

1 Answer
Rui D.
May 3, 2016

#-98#

Explanation:

#((color(teal)(3),color(teal)(1),color(teal)(-2),color(teal)(1)),(color(orange)(1),color(orange)(1),color(orange)(-3),color(orange)(2)),(2,0,2,3),(color(turquoise)(3),color(turquoise)(3),color(turquoise)(1),color(turquoise)(-3)))=#
#-># row2 #-# row1 #-># row2
#-># row4 #-3*# row1 #-># row4

#=((color(gray)(3),color(blue)(1),color(gray)(-2),color(gray)(1)),(-2,color(gray)(0),-1,1),(2,color(gray)(0),2,3),(-6,color(gray)(0),7,-6))#

#=1*(-1)^(1+2)*((-2,-1,1),(2,2,3),(-6,7,-6))#
#=-[24+18+14-(cancel(-12)-42+cancel(12))]#
#=-56-42=-98#

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