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

1 Answer
Mar 21, 2016

Answer:

The inverse of #A#, #A^-1# does not exist because the #detA=0#

Explanation:

The Inverse of #A# is #A^-1# such that #A*A^1=I#
Where I is the identity matrix with
#a_(i,j) = 1 AA-> i=j; 0# otherwise
Quickly check for the determination to check for the existence of #A^-1#
#detA = 1[(5, 1), (4, -4)] - 3[(2, 1), (1, -4)] - [(2, 5), (1, 4)]#
#detA = (-20-4) -3(-8-1)-(8-5) =0#
With #detA=0# the inverse of #A#, #A^-1# does not exist