3 10 0
2 9 7
a
5 15 25 35
b
Trang 24 1 9
AB BA 2 6 3
8 9 2
Trang 3Ma trận A gọi là suy biến nếu det(A) = 0
x 12 16
2 x 8
suy biến x 12 16 0
2 x 8
x 12 x 8 32 0
Trang 4
sin cos sin
sin cos sin
sin cos sin
?
cos sin c
sin cos sin cos sin cos sin os sin cos
cos si
sin cos sin n cos
sin cos sin sin cos cos sin cos sin sin cos cos sin cos s
co
cos n cos sin cos
0 0 0
(tc 3)
Trang 51 0 0 1
2 1 1 0
1 0 1 0
1 1 1 1
?
h h 2 h
h h h
h h h
0 1 1 2
1 0 0 1
0 0 1 1
0 1 1 0
1 0 0 1
0 1 1 2
2
0 0 1 1
0 0 0 2
h h h
Trang 621 22 23
11 12 13
a a a
a a a
a a a
11 31 21
13 33 23
a a a
a a a
a a a
21 22 23
31 32 33
a a a
Tính theo det(A)
21 22 23
11 12 13
31 32 33
a a a
a a a
a a a
11 12 13
21 22 23
31 32 33
a a a
a a a det A
a a a
21 22
11 1
23
31
2 1
2 33
3
3
a a
a
a a
a
a
a
a
21
3
a a a det A
a a a
h h h1 h2
Trang 7m n
X
2 2 nm 2 2
X
2 2 n2 2 2
X
2 2 2 n 2 2
X
2 2 2 2 2 2
X
a 2c 3
3a 4c 5
b 2d 5 3b 4d 9
c 2
d 3
Trang 81 2 3 n
1 3 n
0
0
0
1 2 3
?
1 2 3 n
0 2 6 2n
0 0 3 2n
0 0 0 n
n!
i i 1
h h h
(Với i = 2,3,…,n)
Trang 92 2 3 2
?
2 n 1 2
2 n 1 2 2 3 3
3
2 n 1
2n 1 0 0 1 0 2n 1
1 1 c 2 c n
Trang 10a x x x
x b x x
?
0 x b x x
0 x x c x
0 b x x x b x x
x x x
b x x
a 0 b 0
x c x
0 0 c