How do you find the determinant of #((-7, 0, 0, 3), (-5, -5, 0, 0), (0, -5, 0, 0), (-9, -4, 5, 2))#?

1 Answer
Rui D.
Apr 30, 2016

#-375#

Explanation:

#´[[color(teal)(-7),0,color(orange)(0),3],[color(teal)(-5),-5,color(orange)(0),0],[color(teal)(0),-5,color(orange)(0),0],[color(teal)(-9),-4,color(orange)(5),2]]=#
#-># changing column1 with column3

#=-[[0,0,-7,3],[0,-5,-5,0],[0,-5,0,0],[color(blue)(5),-4,-9,2]]#

#=-5*(-1)^(4+1)*[[0,-7,3],[-5,-5,0],[-5,0,0]]#

#=5*(-5)(-5)*[[0,-7,3],[1,1,0],[1,0,0]]#

#=125*[0-(3)]=-375#

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