(0 )2 1436587@9BAC9EDGF4HI 7P5QHRFTSVU0DXW6F4H

⇐⇒ λ = 1 λ = 2 λ = 3
det(A − λI3) = 0 ⇐⇒ (1 − λ)(2 − λ)(3 − λ) = 0
λ = 0
det A = det(A − 0I3) = (1 − 0)(2 − 0)(3 − 0) = 6 =
0
A
¡ ¨
2 1
2 3
A11 =
A21
= −
A31
=
= 4,
i = 1, 2, 3 j = 1, 2, 3 Aij £¢
¢ (i, j) A
0 −1
2 3
0 −1
2 1
= −2,
= 2,
A12
= −
A22
=
A32
= −
¡
T Aij
A =
¨ ¡
=
A −1 = 1
det A
−1 1 0
1 1 2
3 2 2
1 1
2 3
1 −1
2 3
¢ ¡
1 −1
1 1
4 −1 −2
−2 5 −2
2 −2 2
= −1,
= 5,
= −2,
T
=
4 −2 2
1 A = −1 5 −2
6
−2 −2 2
= −
1 2
2 2
−
1 2
3 2
¢¡
¢
x =
1 1 0
1 1 2
1 2 2
−1 1 0
1 1 2
3 2 2
= − 2
6
A13
=
A23
= −
A33
=
4 −2 2
−1 5 −2
−2 −2 2
= 6 = 0
= − 1
3
1 2
2 2
= −2,
149
1 0
2 2
1 0
1 2
= −2,
= 2.