Find the inverse of the matrix [6 -2 -3][-1 8 -7][4 -4 6]?

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Answer 1 · 2017-09-23T10:39:04

The inverse is #((5/62,3/31,19/124),(-11/124,6/31,45/248),(-7/62,2/31,23/124))#

We write the matrix and the identity matrix side by side and perform the row operations

#((6,-2,-3,|,1,0,0),(-1,8,-7,|,0,1,0),(4,-4,6,|,0,0,1))#

#R2larr(R2)/(-1)# and #R1harrR2#

#((1,-8,7,|,0,-1,0),(6,-2,-3,|,1,0,0),(4,-4,6,|,0,0,1))#

#R2larr(R2-6R1)# and #R3larr(R3-4R1)#

#((1,-8,7,|,0,-1,0),(0,46,-45,|,1,6,0),(0,28,-22,|,0,4,1))#

#R2larr(R2)/(46)# and #R3larr(R3)/(28)#

#((1,-8,7,|,0,-1,0),(0,1,-45/46,|,1/46,3/23,0),(0,1,-11/14,|,0,1/7,1/28))#

#R3larr(R3-R2)# and #R3larr(R3*151/10)#

#((1,-8,7,|,0,-1,0),(0,1,-45/46,|,1/46,3/23,0),(0,0,1,|,-7/62,2/31,23/124))#

#R2larr(R2+45/46R3)#

#((1,-8,7,|,0,-1,0),(0,1,0,|,-11/124,6/31,45/248),(0,0,1,|,-7/62,2/31,23/124))#

#R1larr(R1+8R2)#

#((1,0,7,|,-22/31,17/31,45/31),(0,1,0,|,-11/124,6/31,45/248),(0,0,1,|,-7/62,2/31,23/124))#

#R1larr(R1-7R3)#

#((1,0,0,|,5/62,3/31,19/124),(0,1,0,|,-11/124,6/31,45/248),(0,0,1,|,-7/62,2/31,23/124))#