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

1 Answer
Rui D.
May 3, 2016

#255#

Explanation:

#((color(teal)(5),color(teal)(6),color(teal)(0),color(teal)(0)),(0,1,-1,2),(-3,4,-5,1),(color(orange)(1),color(orange)(6),color(orange)(0),color(orange)(3)))=#
#-># row4 #-# row1 #-># row4

#=((color(blue)(5),color(crimson)(6),0,0),(0,1,-1,2),(-3,4,-5,1),(-4,0,0,3))#

#=5*(-1)^(1+1)((1,-1,2),(4,-5,1),(0,0,3))+6*(-1)^(1+2)*((0,-1,2),(-3,-5,1),(-4,0,3))#

#=5*[-15-(-12)]-6*[4-(40+9)]#
#=5*[-3]-6*[-45]=-15+270=255#

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