How do you find the inverse of #A=##((1, 3, 3), (1, 3, 4), (1, 4, 3))#?

1 Answer
Tony B
Jul 1, 2016

#A^(-1)=[(7,-3,-3),(-1,0,1),(-1,1,0)]#

Explanation:

#[(1,3,3,color(red)(" |"),1,0,0),(1,3,4,color(red)("|"),0,1,0),(1,4,3,color(red)("|"),0,0,1)]#
#Row2-Row1#
#" "darr#

#[(1,3,3,color(red)(" |"),1,0,0),(0,0,1,color(red)("|"),-1,1,0),(1,4,3,color(red)("|"),0,0,1)]#
#Row3-Row1#
#" "darr#

#[(1,3,3,color(red)(" |"),1,0,0),(0,0,1,color(red)("|"),-1,1,0),(0,1,0,color(red)("|"),-1,0,1)]#
#Row1-(3xxRow3)#
#" "darr#

#[(1,0,3,color(red)(" |"),4,0,-3),(0,0,1,color(red)("|"),-1,1,0),(0,1,0,color(red)("|"),-1,0,1)]#
#Row1-(3xxRow2)#
#" "darr#

#[(1,0,0,color(red)(" |"),7,-3,-3),(0,0,1,color(red)("|"),-1,1,0),(0,1,0,color(red)("|"),-1,0,1)]#
#Swapcolor(white)(.) Row2color(white)(.) withcolor(white)(.) Row3#
#" "darr#

#[(1,0,0,color(red)(" |"),7,-3,-3),(0,1,0,color(red)("|"),-1,0,1),(0,0,1,color(red)("|"),-1,1,0)]#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#A^(-1)=[(7,-3,-3),(-1,0,1),(-1,1,0)]#

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