2012-2013
1
.
1.1. = ; B = , 2 + .
. 2 = , 2 + = .
1.2. = , = , = a = 2. +a.
. AT = ;
ATB = × = = ; aC = ;
+a = + = .
1.3 =
:
= -5 + 18 + 6 = 19.( 1 .)
1.4. .
.
.
1.5. .
:
~1 .+3 ~ ~ 1.-2*4~ ~1-2, ~ , rang () = 2.
1.6 , .
:
( )
1.7 :
:
= , B = , A =
-1.
D = det A = 5(4-9) + 1(2 12) 1(3 8) = -25 10 +5 = -30.
11 = = -5; 21 = - = -1; 31 = = -1;
12 = - 22 = 32 = -
13 = 23 = - 33 =
A-1 = ;
:
A×A-1 = =E.
.
= = -1 = × = .
: x =1; y = 2; z = 3.
1.8. A =
.
. A-1 = ;
;
1.9 :
:
D = = 5(4 9) + (2 12) (3 8) = -25 10 + 5 = -30;
Dx = = (28 48) (42 32) = -20 10 = -30.
x = Dx/D = 1;
Dy = = 5(28 48) (16 56) = -100 + 40 = -60.
y = Dy/D = 2;
Dz = = 5(32 42) + (16 56) = -50 40 = -90.
z = Dz/D = 3.
1.10 .
:
.
* =
, :
, : x3 = 2; x2 = 5; x1 = 1.
1.11. , .
.
, - .
, .
1.12.. , .
.
:
.
-1.
-1 , , , - . :
. -1 3. ,
- 2, - . , , . .
, X ,
|
|
.
.
, -2 -3
.
.
.
2. 2 ( ), 3. (3-2=1) . ,
.
, . , .
,
,
.
.
2 3
-1
2. 2 ( ), 3. (3-2=1) . ,
.
, . , .
. , 2, . .
1.13.
.
1. r ( ) .
~
r(A) = r = 2
n = 4 k = n r = 2
k = 2
-
-
2. n r .
1)
2)
.