A= ⎣⎡102−1211−13⎦⎤ , B= ⎣⎡804−31−7−526⎦⎤
Now
A−1= ⎣⎡57−52−545451−53−515152⎦⎤=⎣⎡1.4−0.4−0.80.80.2−0.6−0.20.20.4⎦⎤
BT= ⎣⎡123456789⎦⎤ and (BT)−1= then the determinant of the matrix equals 0 ,Thus, the matrix is not invertible.
B−1=
⎣⎡395392−3911565339173911−1561−394392⎦⎤≈⎣⎡0.120.05−0.020.330.430.28−0.006−0.100.05⎦⎤
B−1×A−1= ⎣⎡57−52−545451−53−515152⎦⎤⋅⎣⎡2532001−5011003310043257−5003−101201⎦⎤=⎣⎡12522−100051−1000107431001−10041−1250123−25001962553⎦⎤=⎣⎡0.176−0.051−0.1070.750.01−0.41−0.0984−0.00760.0848⎦⎤
(7.1)
we got (A−1)−1=A
(7.2)
we got
((BT)−1)T=B−1
(7.8)
we got
(AB) -1 = B-1 A-1
Comments