Algèbre linéaire II Série 15

A∈(n×n, Z)A
B∈(n×n, Z)A·B=Endet A= 1
det A=−1
Ax =b
A=
1 2 2
4 2 9
4 5 7
, b =
2
6
4
.
A, B ∈(n×n, R)
A#T=AT#
(A·B)#=B#·A#
det A#= (det A)n−1
M=
123
014
001
A#A
T:R3−→ R3
−14 43 −22
1 20 −14
3 25 −21
.
T
T

R3
T
A= (aij )∈(n×n, R)Piaij = 1 1 ≤j≤n
A1
R
A∈(n×n, R)R A
det A R
A
A∈(n×n, R)A A#
T:V−→ V0T T
T:V−→ V0T T