[ ] [ ]
3 2 2 1
1 4 -1
îÅ‚ Å‚Å‚ îÅ‚0 Å‚Å‚
3 2 1 3 0 1
ðÅ‚ ûÅ‚ ðÅ‚ ûÅ‚
4 7 1 2 -1 2
-1 2 0 0 5 1
îÅ‚ Å‚Å‚ îÅ‚ Å‚Å‚ îÅ‚ Å‚Å‚
3 4 2 5 2 0 2 1 1 0 2 1
ïÅ‚ śł ïÅ‚ śł ïÅ‚ śł
7 1 0 2 0 1 2 0 0 2 3 0
ïÅ‚ śł ïÅ‚ śł ïÅ‚ śł
A = , B = , C = .
ðÅ‚ ûÅ‚ ðÅ‚ ûÅ‚ ðÅ‚ ûÅ‚
0 3 1 1 2 2 1 1 1 4 1 1
2 0 4 0 2 2 1 -2 2 8 2 -4
îÅ‚ Å‚Å‚
[ ]
1 -2 -1
-1 -1
ðÅ‚ ûÅ‚
A = , B = 2 -1 -1 .
3 2
3 -4 2
îÅ‚ Å‚Å‚
îÅ‚ Å‚Å‚
2 1 11 2
1 1 1 3
ïÅ‚ śł
1 0 4 -1
ðÅ‚ ûÅ‚ ïÅ‚ śł
2 -1 1 1
ðÅ‚ ûÅ‚
11 4 56 5
0 3 1 5
2 -1 5 6
Å„Å‚
Å„Å‚ Å„Å‚ Å„Å‚
ôÅ‚
ôÅ‚2x1 + x2 - x3 + x4 = 0 ôÅ‚ 1 + 2x2 + x3 = 5 ôÅ‚ 1 + x2 + x3 + x4 = 2
ôÅ‚ ôÅ‚
1
òÅ‚x + x2 + x3 = 2 òÅ‚3x + x2 + x3 + x4 = 0 òÅ‚x òÅ‚x
1
x1 - x2 - x3 = 0 2x1 + x2 - x3 = 4 2x1 - x2 - 2x3 + x4 = 0
ôÅ‚
ół2x + x2 + 3x3 = 1 ôÅ‚3x1 + x2 - x3 + x4 = 0 ôÅ‚ - x2 - 2x3 = -1 ôÅ‚ - 3x2 - 5x3 + x4 = 1
ôÅ‚ ółx ół3x
ôÅ‚
ół
1 1 1
x1 + x4 = 0
(5+i)(3+5i)
6.1 Re[(4 + i)(5 + 3i) - (3 + i)(3 - i)], 6.2 , 6.3 i-77, 6.4 (3 + i)3 - (3 - i)3,
2i
" " "
4 3
6.5 (1 + i)100, 6.6 -16, 6.7 64i, 6.8 i + 1.
"
1+i
7.1 -4i, 7.2 3 - 3i, 7.3 -1 + i 3, 7.4 .
1-i
z2 - 5z + 4 + 10i = 0
iz3 - i3 = 0
" "
" "
3 3
2n5-3n7+8n 1-5n3 1+2n2- 1+4n2
9.1 an = , 9.2 an = , 9.3 an = , 9.4 an = n3 + 3 - n3 - 3,
2n3+6n7-8n+4 2+n2 n
2
( )2n +5
2n+(-1)n
n2+3 27log3 n
9.5 an = 2-n cos(nĄ), 9.6 an = , 9.7 an = , 9.8 an = ,
n2+1 16log2 n n
"
-8n-1 5·32n-1 n
9.9 an = , 9.10 an = , 9.11 an = 10n + 9n + 8n.
7n+1 4·9n+7
10.1 y2 2 + 3y2 + 2y = 0, 10.2 y2 2 + 12y2 + 36y = 0, 10.3 y2 2 + 2y2 + 5y = 0, 10.4 y2 2 - 8y2 + 16y = 0,
10.5 y2 2 - 5y2 + 6y = 2x + 1, 10.6 y2 2 - y = sin x, 10.7 y2 2 - 6y2 = cos 2x.
11.1 y2 2 + 4y = 0, y(0) = 0, y2 (0) = 2,
11.2 y2 2 - 4y2 + 3y = e2x sin x, y(0) = 1, y2 (0) = 1.
2
y
12.1 f(x, y) = ex sin y, 12.2 f(x, y) = arccos , 12.3 f(x, y, z) = xy - zx.
x
y2
x2
13.1 36y2 - 4x2 - 9z2 - 144y + 108 = 0, 13.2 - y2 = z + 1, 13.3 x2 - + z2 = 1,
4 4
13.4 z = 4 - x2 - y2, 13.5 y = x2 + 2z2, 13.6 x2 + z2 = 9.
"" n "" 5 log n "" (2n)!(3n)! "" "
3
"n +1
14.1 , 14.2 , 14.3 , 14.4 ,
3
n=1 n2 n=1 n4 n=1 5n! n=1
n7+1
îÅ‚ Å‚Å‚
[ ]
13 3 8
4 3
ðÅ‚ ûÅ‚
26 -2 19
-2 1
1 -2 3
|A| = -262 |B| = 30 |C| = 84
îÅ‚ Å‚Å‚
[ ]
-6 8 1
2 1
1
ðÅ‚ ûÅ‚
A-1 = , B-1 = -7 5 -1
13
-3 -1
-5 -2 3
2 3
x1 = 1 x2 = 2 x3 = -1 x1 = x2 = x3 = x4 = 0 x1 = t + 1 x( = 2 - t x3 =)t
2
" " ( 5Ä„ 5Ä„ )
Ä„ Ä„
7 14 - 5i -i 52i -250 4i -4i w0 = 2 2 cos + i sin w1 = 2 2 cos + i sin
8 8 8 8
" ( ) " ( ) " ( )
1 1
6
9Ä„ 9Ä„ 13Ä„ 13Ä„ Ä„ Ä„
w2 = 2 2 cos + i sin = 2 2 cos + i sin w0 = 2 cos + i sin w1 = 2- 3 - 2- 3
i
8 8 8 8 12 12
" ( )w3
6 -7Ä„ -7Ä„
w3 = 2( cos + i sin
12 12
) " ( ) ( )
-Ä„ -Ä„ Ä„ -Ä„ 2Ä„ 2Ä„ Ä„ Ä„
4 cos + i sin 3 2 cos + i sin 2 cos + i sin cos + i sin
4 4 4 4 3 3 2 2
" "
1+5i 9-5i 1 3 1 3
z1 = z2 = z1 = + i z2 = -1 z3 = - i
2 2 2 2 2 2
"
1 5
- -" 2 - 2 0 0 e4 0 2 -" 10
2 4
y(x) = C1e-2x + C2e-x y(x) = C1e-6x + C2xe-6x y(x) = e-xC1 sin 2x + e-xC2 cos 2x
1 1
y(x) = C1e4x + C2xe4x y(x) = (4 + 3x) + C1e2x + C2e3x y(x) = C1ex + C2e-x - sin x
9 2
1 1 3
y(x) = e6xC1 + C2 - cos 2x - sin 2x
6 40 40
1 3 1
y(x) = sin 2x y(x) = e3x + ex - e2x sin x
4 4 2
2 2
"f "f "f y "f -1 "f "f
" "
= ex sin y2x sin y = ex sin yx2 cos y = = = yxy-1-zx ln z = xy ln x
"x "y "x "y
x x2-y2 "y x2-y2 "x
"f
= -xzx-1
"z