(x1, x2,..., xn) n n- , xi (i = ) - , , .
, , 50 , 100 , 10 , 50 150 , (50, 100, 10, 50, 150), . . , .
, , (3, 2, 5, 0, 1) ≠ (2, 3, 5, 0, 1).
x = (x1, x2,...,xn) λ x = (λx1, λx2,..., λxn).
x = (x1, x2,...,xn) y = (y1, y2,...,yn)
x + y = (x1 + y1, x2 + y2,..., xn + yn).
N- Rn n- , .
n- : (). , . , n; , ,
x = (x1, x2,..., xn),
xi i- , . , , .
C = { x = (x1, x2,..., xn)| xi ≥ 0, i = }.
e1, e2,..., em n- , λ1, λ2,..., λm, , λ1e1 + λ2e2 +... + λmem = 0;
, , λ1 = λ2 =... = λm = 0. R3, , .
1. , , , .
2. , , , .
3. , , , .
a, b, c , a, b, c . B a, b, c - . ( ) .
|
|
e1, e2, e3 R3 , e1, e2, e3 - . a ,
= x1 e1 + x2 e2 + x3 e3, (1.1)
x1, x2, x3 (1.1) a e1, e2, e3 a(x1, x2, x3). e1, e2, e3 , , x1, x2, x3 - . i, j, k.
, R3 {0, i, j, k}.
b c, :
1. c , a b, . . |c| = |a||b| sin (a^b).
2. c a b.
3. a, b c, , .
c c = [ab] c = a x b.
a b , sin(a^b) = 0 [ab] = 0, , [aa] = 0. : [ij] = k, [jk] = i, [ki] = j.
a b i, j, k a(a1, a2, a3), b(b1, b2, b3),
b c, a b c.
a, b c i, j, k a(a1, a2, a3),
b(b1, b2, b3), c(c1, c2, c3),
- , , .
, , ;
a, b, c - , abc < 0 V = - abc, V = |abc|.
, , . , , 0. r= - , , ||, || .