1. 2 : :
:
I ( ).
; - ; - - :
= ; = ; = .
:
* = . (1)
( ¹0), . (1) , :
**= *.
*= (- ), =,
= * (2)
(2) . , :
:
= 1*3*2 + (-2)*(-1)*1 + 2*1*(-1) 3*1*1 1*(-1)*(-1) 2*2*(-2)= 10;
, :
, , i- j- ¢, :
(2) :
= = *= * =
.
II ( ):
, ..
.
~
.. , , . , , . .
, , . .
~ , , . , .. , - .
0 1 + 0 2 + 10 3 = -20, 10 3 = -20, 3= -2.
, 3 = -2,
0 1 + (-7) 2 +3 3 =-6, -72 + 3(-2)= -6, -72 =0, 3=0.
1
1 1 2 2 + 3 =1, 1 20 2 =1, 1=3
: 1=3, 2=0, 3= -2.
- , , , .
(), ,(),
=2i 2j+k; = i+j+3k; = i+3j 4k.
:
.
1.
|
|
, , .
()= 1× (2×1) + 1×(2×3) + 3×(2×(-4)) = 2+6 24 = -16.
2.
, , , .
,
: () =-16; = ; () = 228.
3. : (-4;8),(5;-4),(10;6). : 1) ; 2) , ; 3) ; 4) , , ; 5) ; 6) .
: 1. d 1(1, 1) 2(2,2)
|12| =
, :
=
2. , 1(1, 1) 2(2,2),
, :
-12x - 48 = 9y 72, 4x +3y 8 =0 (AB).
, :
x+7y- 52=0 (AC).
- a , k1 k2, :
k1 k2 , y=kx+ b, k .
: , : , k1= kAB = - , k2=kAC = - ,
, Ð = arctg 1 = 45.
4. + += 0. , . , , , .
1 +1 +1=0. + += 0 (, ) , , .. , , . , , . , , , .
4x +3y 8 =0 (10;6). (4;3) 4 +3 +=0.
. 4× 10+3 ×6 + =0, 40+18+=0, = - 58.
, ,
4x +3y -58=0.
5. CD , . ,
, m,k - . , CD
,
3x-30=4y-24, 3x-4y-6=0 (CD).
6. , . (-4; 8) , BC
(7,5; 1) (-4, 8), AM
7x+11,5y+64=0.(AM)
:
1. =15;
2. 4 x +3y 8 =0$
3. Ða = 45;
4. 4x+3y+25 = 0;
5. - , CD=10;
6. 7x+11,5y+64=0.
4. ABX=C,
|
|
= , = , =
: . .
, . , , .. i- j- .
r11= 12 +11+(-3)4=-9, r21= 32+21+24=16,
r12= 13 + 11 +(-3) 5=-11, r22= 33 +21+25=21,
r13= 11 +1(-4)+(-3) (-3)=6, r23=31+2(-4)+2(-3)=-11,
r31=12+(-1) 1+54=21, r32=13+(-1) 1+55=27,
r33=11+(-1) (-4)+5(-3)=-10.
R= . RX=C R-1 R. X= R 1 C.
.
1. R
=-921(-10)+(-11) (-11) 21+16276 62121-(- 9)(-11) 27 16(-11) (-10)=
=1890+2541+2592 2646 26731760=-56.
2. , .. .
R=
3.
4.
.
X. R-1 .
: = .
5. , , .
:
, , . , , .. .
: 5 . .
6. : (1,2,3); (5,2,2); (2,4,3); (4,5,8). :
1. ;