How do you find the inverse of #A=##((1, 1, -1), (0, 1, 0), (1, 0, 1))#?

1 Answer
Dec 16, 2016

Answer:

#=>A^(-1) = ((1/2,-1/2,1/2),(0,1,0),(-1/2,1/2,1/2))#

Explanation:

Write as:

#((1,1,-1,"|",1,0,0),(0,1,0,"|",0,1,0),(1,0,1,"|",0,0,1)) #
#" "R_1-R_2#
#" "R_1-R_3#
#" "darr#

#((0,0,-2,"|",1,-1,-1),(0,1,0,"|",0,1,0),(1,0,1,"|",0,0,1)) #
#" "R_1-:(-2)#
#" "darr#

#((0,0,1,"|",-1/2,1/2,1/2),(0,1,0,"|",0,1,0),(1,0,1,"|",0,0,1)) #
#" "R_3-R_1#
#" "darr#

#((0,0,1,"|",-1/2,1/2,1/2),(0,1,0,"|",0,1,0),(1,0,0,"|",1/2,-1/2,1/2)) #
#" Swap "R_3" with "R_1#
#" "darr#

#((1,0,0,"|",1/2,-1/2,1/2),(0,1,0,"|",0,1,0),(0,0,1,"|",-1/2,1/2,1/2)) #

#color(white)(.)#

#=>A^(-1) = ((1/2,-1/2,1/2),(0,1,0),(-1/2,1/2,1/2))#