îÅ‚ Å‚Å‚ îÅ‚ Å‚Å‚
8 3 10 13 1 -2 1
ðÅ‚ ûÅ‚ ðÅ‚ ûÅ‚
1 0 1 1 , 2 1 -2
3 1 4 5 -3 5 -2
Å„Å‚
x1
òÅ‚ - 2x2 + 2x3 - 4x4 + x5 - 4x6 = -4
2x1 + x2 + 4x3 - 3x4 - 2x5 - x6 = 9
ół
-3x1 + 5x2 - 6x3 + 11x4 - 2x5 + 11x6 = 9
Å„Å‚
x1 + 8x2 + 3x3 = 23
òÅ‚
x1 + 10x2 + 4x3 = 28
ół
x1 + 7x2 + 5x3 = 18
Å„Å‚
2x1 + 4x2 + 5x3 = 3
ôÅ‚
ôÅ‚
òÅ‚
3x1 + 6x2 + 8x3 = 2
ôÅ‚ -5x1 - 10x2 - 14x3 = 0
ôÅ‚
ół
4x1 + 8x2 + 11x3 = 1
W (x)
W (-1) = 0 W (1) = -4 W (2) = -3 W (0) = 1
z
z2 = 15 + 8i
iz2 - 3iz + 3i - 1 = 0
2z + 3z - Rez = 8 - 3i
|z| + 3z = 2 + 6i
4+5i
z =
3i-4
z = (i5 + i6)20
z
(1 + i) z2 + (3 - 5i) z - 6 = 0
(3 + 2i) z2 - 13z + 9 - 7i = 0
(1 - 2i) z2 - (9 + 2i) z + 10i = 0
(1 + i) z2 + (1 - 3i) z + 6i = 0
(1 + i) z2 + (3 + 3i) z + 2 + 4i = 0
iz2 - 3iz + 3i - 1 = 0
Å„Å‚
x + 2y + iz = 5
òÅ‚
ix + (1 + i)y + 3z = 2 + i
ół
2x + (3 - i)y - 2iz = 6 - 2i
Å„Å‚
x1 + (1 + i) x2 + (2 + 2i) x3 + 2x4 = 2 - 2i
òÅ‚
(1 - i) x1 + 2x2 + 3x3 + (-1 + i) x4 = 2
ół
(2 - i) x1 + (3 + i) x2 + (5 + 2i) x3 + ix4 = 4 - i
 R3
A = {(x, y, z) ; 2x = 4y - 3z} ,
B = {(x, y, z) ; 2x + 5y - 3z = 2} ,
C = {(x, y, z) ; y = 2x2 - z} ,
D = {(x, y, z) ; 2x2 + 5z2 = 0}
V = lin{(1, 2, 3, 4), (2, 3, 5, 6)} W = lin{(1, 3, 3, 5), (-2, 1, -2, 1)}
V )" W
V W
x1 - 2x2 + 3x3 - 4x4 = 0 x1 - 3x2 + 3x3 - 4x4 = 0
V : W :
2x1 - 4x2 + 3x3 - 5x4 = 0 2x1 + 4x2 + 3x3 + 2x4 = 0
V )" W V, W V )" W
{(2, 3, 2) , (3, 4, 2) , (1, 2, 1)} :
(1, 0, 0)
(1, 2, 3)
(1, 2, 1)