Векторная алгебра. Машанов В.И - 24 стр.

UptoLike

Задача 13
Доказать, что векторы cba
r
r
r
,, линейно независимы и найти координаты вектора d
r
в базисе
.,, cba
r
r
r
N
a
r
b
r
c
r
d
r
1
)3,2,1(
a
r
)0,1,3( b
r
)1,1,2(
c
r
)5,2,3( d
r
2
)4,1,2(
a
r
)2,0,1(b
r
)5,2,3(
c
r
)9,0,4(d
r
3
)0,1,3(
a
r
)3,2,4(b
r
)1,3,5(
c
r
)8,5,7( d
r
4
)1,2,4(
a
r
)1,0,3( b
r
)2,1,3(
c
r
)1,7,9( d
r
5
)1,2,3(
a
r
)0,1,2( b
r
)2,2,4(
c
r
)0,3,4( d
r
6
)3,1,2(
a
r
)4,2,1( b
r
)2,0,3(c
r
)4,2,1( d
r
7
)4,2,3(
a
r
)1,1,2( b
r
)3,3,1(
c
r
)5,1,4( d
r
8
)3,1,2(
a
r
)4,2,3( b
r
)2,3,1(
c
r
)1,5,1(d
r
9
)2,3,1(
a
r
)1,1,2( b
r
)2,4,3(
c
r
)5,9,3( d
r
10
)3,1,2(
a
r
)2,2,1(b
r
)1,3,1(
c
r
)1,3,6(d
r
11
)1,3,2(
a
r
)0,2,1(b
r
)1,5,3(c
r
)2,6,3(d
r
12
)1,1,3(
a
r
)1,2,2(b
r
)3,0,4(c
r
)2,5,3( d
r
13
)2,2,3(
a
r
)3,1,2( b
r
)4,3,5(
c
r
)3,2,3( d
r
14
)1,2,4(
a
r
)1,1,3( b
r
)2,1,7(c
r
)1,5,5( d
r
15
)2,3,1(
a
r
)1,1,2( b
r
)3,3,2(
c
r
)4,6,6( d
r
16
)1,0,2(
a
r
)3,2,1( b
r
)4,2,1(
c
r
)1,0,6( d
r
17
)1,1,3(
a
r
)3,2,2( b
r
)4,1,5(
c
r
)4,5,5( d
r
18
)1,2,4(
a
r
)2,1,3( b
r
)1,0,2(
c
r
)1,3,3( d
r
19
)2,1,3(
a
r
)3,2,2( b
r
)1,3,5(
c
r
)7,2,2( d
r
20
)1,4,2(
a
r
)23,1( b
r
)3,7,1(
c
r
)3,7,5( d
r
21
)2,1,3(
a
r
)1,3,2( b
r
)3,4,1(
c
r
)9,7,6( d
r
22
)2,1,4(
a
r
)1,2,3( b
r
)3,3,1(
c
r
)7,2,7( d
r
23
)2,3,1(
a
r
)1,1,2( b
r
)1,1,3(
c
r
)6,9,7( d
r
24
)1,2,2(
a
r
)2,1,3( b
r
)1,3,5(
c
r
)3,2,2( d
r
25
)2,1,3(
a
r
)1,2,2( b
r
)2,3,1(
c
r
)1,3,3(d
r
26
)3,1,2(
a
r
)1,2,3( b
r
)3,2,1(c
r
)0,2,2( d
r
27
)2,2,3(
a
r
)2,1,1( b
r
)1,1,2(
c
r
)1,2,4( d
r
28
)1,1,2(
a
r
)2,2,1( b
r
)1,3,3(
c
r
)3,1,2( d
r
29
)3,2,1(
a
r
)2,1,2( b
r
)1,3,3(
c
r
)6,2,2( d
r
30
)2,1,4(
a
r
)1,2,3( b
r
)0,1,1(c
r
)3,1,6(d
r
Задача 13
                      r r r                                                     r
Доказать, что векторы a , b , c   линейно независимы и найти координаты вектора d в базисе
r r r
a, b , c.
       r                          r                     r                   r
N a                               b                     c                   d
       r                          r                     r                   r
 1 a (1,−2,3)                     b (3,−1,0)            c (2,−1,1)          d (3,−2,5)
       r                          r                     r                   r
 2 a (2,−1,4)                     b (1,0,2)             c (3,−2,5)          d (4,0,9)
       r                          r                     r                   r
 3 a (3,−1,0)                     b (4,2,3)             c (5,3,−1)          d (7,−5,8)
       r                          r                     r                   r
 4 a (4,2,−1)                     b (3,0,−1)            c (3,1,−2)          d (9,7,−1)
       r                          r                     r                   r
 5 a (3,−2,1)                     b (2,−1,0)            c (4,−2,2)          d (4,−3,0)
       r                          r                     r                   r
 6 a (2,−1,3)                     b (1,−2,4)            c (3,0,2)           d (1,−2,4)
       r                          r                     r                   r
 7 a (3,2,−4)                     b (2,1,−1)            c (1,3,−3)          d (4,1,−5)
       r                          r                     r                   r
 8 a (2,−1,3)                     b (3,−2,4)            c (1,−3,2)          d (1,5,1)
       r                          r                     r                   r
 9 a (1,−3,2)                     b (2,−1,1)            c (3,−4,2)          d (3,−9,5)
       r                          r                     r                   r
10 a (−2,1,3)                     b (1,2,2)             c (−1,3,1)          d (−6,3,1)
       r                          r                     r                   r
11 a (2,3,−1)                     b (1,2,0)             c (3,5,1)           d (3,6,2)
       r                          r                     r                   r
12 a (3,1,−1)                     b (2,2,1)             c (4,0,3)           d (3,5,−2)
       r                          r                     r                   r
13 a (3,2,−2)                     b (2,1,−3)            c (5,3,−4)          d (3,2,−3)
       r                          r                     r                   r
14 a (4,2,−1)                     b (3,−1,1)            c (7,1,2)           d (5,5,−1)
       r                          r                     r                   r
15 a (1,3,−2)                     b (2,1,−1)            c (2,3,−3)          d (6,6,−4)
       r                          r                     r                   r
16 a (2,0,−1)                     b (1,2,−3)            c (1,2,−4)          d (6,0,−1)
       r                          r                     r                   r
17 a (3,1,−1)                     b (2,2,−3)            c (5,1,−4)          d (5,5,−4)
       r                          r                     r                   r
18 a (4,−2,1)                     b (3,−1,2)            c (2,0,−1)          d (3,−3,1)
       r                          r                     r                   r
19 a (3,−1,2)                     b (2,−2,3)            c (5,−3,1)          d (2,−2,7)
       r                          r                     r                   r
20 a (2,4,−1)                     b (1,3 − 2)           c (1,7,−3)          d (5,7,−3)
       r                          r                     r                   r
21 a (3,1,−2)                     b (2,3,−1)            c (1,4,−3)          d (6,7,−9)
       r                          r                     r                   r
22 a (4,1,−2)                     b (3,2,−1)            c (1,3,−3)          d (7,2,−7)
       r                          r                     r                   r
23 a (1,3,−2)                     b (2,−1,1)            c (3,1,−1)          d (−7,9,−6)
       r                          r                     r                   r
24 a (2,−2,1)                     b (3,−1,2)            c (5,−3,1)          d (2,−2,3)
       r                          r                     r                   r
25 a (3,−1,2)                     b (2,−2,1)            c (1,−3,2)          d (3,3,1)
       r                          r                     r                   r
26 a (2,−1,3)                     b (3,−2,1)            c (1,2,3)           d (−2,−2,0)
       r                          r                     r                   r
27 a (3,−2,2)                     b (1,−1,2)            c (2,−1,1)          d (4,−2,1)
       r                          r                     r                   r
28 a (2,−1,1)                     b (1,−2,2)            c (3,−3,1)          d (2,−1,3)
       r                          r                     r                   r
29 a (1,−2,3)                     b (2,−1,2)            c (3,−3,1)          d (2,−2,6)
       r                          r                     r                   r
30 a (4,−1,2)                     b (3,−2,1)            c (1,1,0)           d (6,1,3)