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

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Answer 1 · 2017-08-18T08:54:17

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

To calculate the inverse, we proceed as follows

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

#R1harrR2#, #=>#,#((-1,8,-7,:,0,1,0),(6,-2,-3,:,1,0,0),(4,-4,6,:,0,0,1))#

#R3larrR3+4R1#, #=>#,#((-1,8,-7,:,0,1,0),(6,-2,-3,:,1,0,0),(0,28,-22,:,0,4,1))#

#R2larrR2+6R1#, #=>#,#((-1,8,-7,:,0,1,0),(0,46,-45,:,1,6,0),(0,28,-22,:,0,4,1))#

#R1larr(R1)/(-1)#, #=>#,#((1,-8,7,:,0,-1,0),(0,46,-45,:,1,6,0),(0,28,-22,:,0,4,1))#

#R3larrR3(*1/28)#, #=>#,#((1,-8,7,:,0,-1,0),(0,46,-45,:,1,6,0),(0,1,-11/14,:,0,1/7,1/28))#

#R2larrR2/(46)#, #=>#,#((1,-8,7,:,0,-1,0),(0,1,-45/46,:,1/46,3/23,0),(0,1,-11/14,:,0,1/7,1/28))#

#R3larrR3-R2#, #=>#,#((1,-8,7,:,0,-1,0),(0,1,-45/46,:,1/46,3/23,0),(0,0,31/161,:,-1/46,2/161,1/28))#

#R3larrR3*(161/31)#, #=>#,#((1,-8,7,:,0,-1,0),(0,1,-45/46,:,1/46,3/23,0),(0,0,1,:,-7/62,2/31,23/124))#

#R2larrR2+(45/46)R3#, #=>#,#((1,-8,7,:,0,-1,0),(0,1,0,:,-11/124,6/31,45/248),(0,0,1,:,-7/62,2/31,23/124))#

#R1larrR1+(8)R2#, #=>#,#((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))#

#R1larrR1-(7)R3#, #=>#,#((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))#

Verification

#((5/62,3/31,19/124),(-11/124,6/31,45/248),(-7/62,2/31,23/124))#*#((6,-2,-3),(-1,8,-7),(4,-4,6))#

#=((1,0,0),(0,1,0),(0,0,1))#