2.
Rn , n (1, 2, , n) =` a, .
Rn : ..
2.1.
` 1, ` 2, ¼, ` n l 1, l 2, ¼, l n
`b = l 1 ` a 1 + l 2 ` a 2 + ¼ + l n ` a n.
2.2. {` 1, ` 2, ¼, ` n } , . ( ).
2.3. B = {` b 1, ` b 2, ¼, ` b n }Ì Rn
Rn, ` Î Rn :
` = 1 ` b1 + 2 ` b2 + + n ` bn, xi Î Rn; i = 1, 2, , n.
. , Rn , ∆ (` b 1, ` b 2, ¼, ` b n) ≠ 0.
Rn
` 1 = (1, 0, 0,, 0); ` 2 = (0, 1, 0,, 0); ` n = (0, 0, 0,, 1)
2.4.
: .
1. ();
2. ();
3. ( );
4.
Rn
2.5. Rn
.
1. , , .
2. .
3. : .
2.6. , , :
. |
2.7. ,
( ) , , .
R3.
C
2.8. ` ` b R3 ` (. ):
) , ` ` b, ;
) ` ;
) , ` ` b
` ( , (` , ` b, ` c) ).
` = ` ´ ` b.
|
|
. ( ).
` a = (1, 2, 3), ` b = (b1, b2 , b3), ` a ´ ` b :
` i, ` j, ` k R3: .
1. ();
2. ();
3. ;
4. , .