How do you find the determinant of #((44, 32, 18, 6), (-2, 10, 15, 5), (21, 12, -12, 4), (-8, -16, 4, 9))#?

1 Answer
May 1, 2016

Answer:

#-148,116#

Explanation:

#[[44,32,18,color(violet)(6)],[-2,10,15,color(violet)(5)],[21,12,-12,color(violet)(4)],[-8,-16,4,color(violet)(9)]]=#

#=6*(-1)^(1+4)[[-2,10,15],[color(teal)(21),color(teal)(12),color(teal)(-12)],[color(magenta)(-8),color(magenta)(-16),color(magenta)(4)]] +5*(-1)^(2+4)[[color(blue)(44),color(blue)(32),color(blue)(18)],[color(teal)(21),color(teal)(12),color(teal)(-12)],[color(magenta)(-8),color(magenta)(-16),color(magenta)(4)]]+4*(-1)^(3+4)[[color(blue)(44),color(blue)(32),color(blue)(18)],[-2,10,15],[color(magenta)(-8),color(magenta)(-16),color(magenta)(4)]]+9*(-1)^(4+4)[[color(blue)(44),color(blue)(32),color(blue)(18)],[-2,10,15],[color(magenta)(21),color(magenta)(12),color(magenta)(-12)]]=#

#=-6*3*4[[-2,10,15],[color(teal)(7),color(teal)(4),color(teal)(-4)],[color(magenta)(-2),color(magenta)(-4),color(magenta)(1)]] +5*2*3*4[[22,16,9],[color(teal)(7),color(teal)(4),color(teal)(-4)],[color(magenta)(-2),color(magenta)(-4),color(magenta)(1)]]-4*2*4[[22,16,9],[color(teal)(-2),color(teal)(10),color(teal)(15)],[color(magenta)(-2),color(magenta)(-4),color(magenta)(1)]]+9*2*3[[22,color(orange)(16),color(red)(9)],[-2,color(orange)(10),color(red)(15)],[7,color(orange)(4),color(red)(-4)]]=#

#=-72[[-2,color(violet)(10),15],[5,color(violet)(0),-3],[-2,color(violet)(-4),1]] +120[[22,color(violet)(16),9],[5,color(violet)(0),-3],[-2,color(violet)(-4),1]]-32[[color(violet)(22),16,9],[0,color(blue)(14),color(blue)(14)],[color(violet)(-2),-4,1]]+54[[22,color(violet)(25),9],[-2,color(violet)(25),15],[7,color(violet)(0),-4]]=#

#=-72*2[[-2,5,15],[5,0,-3],[-2,-2,1]] +120*4[[22,4,9],[5,0,-3],[-2,-1,1]]-32*2*14[[11,16,9],[0,1,1],[-1,-4,1]]+54*25[[22,1,9],[-2,1,15],[7,0,-4]]=#

#=-144[30-150-(-12+25)]+480[24-45-(66+20)]-896[11-16-(-9-44)]+1350[-88+105-(63+8)]#
#=-144[-120-13]+480[-21-86]-896[-5+53]+1350[17-71]#
#=144*133-480*107-896*48-1350*54#
#=19152-51360-43008-72900=-148116#