How do you find the inverse of #A=##((0, 2, 4), (1, 3, 3), (1, 5, 8))#?

1 Answer
Nov 1, 2017

Answer:

The inverse is #A^-1=((-9/2,-2,3),(5/2,2,-2),(-1,-1,1))#

Explanation:

Proceed as follows

Our matrix is #A=((0,2,4),(1,3,3),(1,5,8))#

Write side by side #A# and #I#

#((0,2,4),(1,3,3),(1,5,8))((1,0,0),(0,1,0),(0,0,1))#

Perform the following row operations

#R1harrR3#

#((1,5,8),(1,3,3),(0,2,4))((0,0,1),(0,1,0),(1,0,0))#

#R2larrR2-R1#

#((1,5,8),(0,-2,-5),(0,2,4))((0,0,1),(0,1,-1),(1,0,0))#

#R3larrR3+R2#

#((1,5,8),(0,-2,-5),(0,0,-1))((0,0,1),(0,1,-1),(1,1,-1))#

#R3larr(R3)xx(-1)#

#((1,5,8),(0,-2,-5),(0,0,1))((0,0,1),(0,1,-1),(-1,-1,1))#

#R2larr(R2)xx(-1)#

#((1,5,8),(0,2,5),(0,0,1))((0,0,1),(0,-1,1),(-1,-1,1))#

#R2larr(R2)-5(R3)#

#((1,5,8),(0,2,0),(0,0,1))((0,0,1),(5,4,-4),(-1,-1,1))#

#R1larr(R1)-8(R3)#

#((1,5,0),(0,2,0),(0,0,1))((8,8,-7),(5,4,-4),(-1,-1,1))#

#R2larr(R2)/2#

#((1,5,0),(0,1,0),(0,0,1))((8,8,-7),(5/2,2,-2),(-1,-1,1))#

#R1larr(R1)-5(R2)#

#((1,0,0),(0,1,0),(0,0,1))((-9/2,-2,3),(5/2,2,-2),(-1,-1,1))#

Therefore,

#A^-1=((-9/2,-2,3),(5/2,2,-2),(-1,-1,1))#