1
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2) , .. (), (), :
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3) , .. (+) (+), :
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( + ) = + .
4) , a :
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6) , det (AB) = detA×detB.
det (, ) .
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AT = ; ATB = × = = ;
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. = = .
= × = .
= × = 2×1 + 4×4 + 1×3 = 2 + 16 + 3 = 21.
. = , =
= × = = .
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det A = ,
1 , k . , , .. , .
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, , .. :
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1.
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det A = det AT;
2. det (A B) = det A det B.
3. det (AB) = detA×detB
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9. - : d = d1 d2, e = e1 e2, f = f1 f2, :
. =
= -5 + 18 + 6 = 19.
:. = , = . det (AB).
1- : det A = 4 6 = -2; det B = 15 2 = 13; det (AB) = det A ×det B = -26.
2- : AB = , det (AB) = 7×18 - 8×19 = 126
152 = -26.
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, -1= .
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ji - ji .
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det A = 4 - 6 = -2.
M11=4; M12= 3; M21= 2; M22=1
x11= -2; x12= 1; x21= 3/2; x22= -1/2
, -1= .
C .
:
1) (A-1)-1 = A;
2) (AB)-1 = B-1A-1
3) (AT)-1 = (A-1)T.
, 33.
Enter.
: Maple (Ó Waterloo Maple Inc.) , MapleV Release 4.
. = , 3.
2 = = = ; A3 = = .
, .
. .
= -1
= -1(6 4) 1(9 1) + 2(12 2) = -2 8 + 20 = 10.
= = 2(0 2) 1(0 6) = 2.
= = 2(-4) 3(-6) = -8 + 18 = 10.
: -10 + 6 40 = -44.
.
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.. -1× = , × = -1×
= -1×
, .
. :
= , B = , A =
-1.
D = det A = 5(4-9) + 1(2 12) 1(3 8) = -25 10 +5 = -30.
M11 = = -5; M21 = = 1; M31 = = -1;
M12 = M22 = M32 =
M13 = M23 = M33 =
A-1 = ;
C :
A×A-1 = =E.
.
= = -1 = × = .
: x =1; y = 2; z = 3.
, , .
.
( (1704-1752) )
, . , . , , .. .
, 0.
det A ¹ 0;
, - , - , - , . .
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. n n
, , :
xi = Di/D,
D = det A, Di , i bi.
Di =
.
A = ; D1= ; D2= ; D3= ;
x1 = D1/detA; x2 = D2/detA; x3 = D3/detA;
. :
D = = 5(4 9) + (2 12) (3 8) = -25 10 + 5 = -30;
D1 = = (28 48) (42 32) = -20 10 = -30.
x1 = D1/D = 1;
D2 = = 5(28 48) (16 56) = -100 + 40 = -60.
x2 = D2/D = 2;
D3 = = 5(32 42) + (16 56) = -50 40 = -90.
x3 = D3/D = 3.
, , .
, .. bi = 0, D¹0 x1 = x2 = = xn = 0.
D = 0 .
:
; : x = 0; y = 0; z = -2.
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, , . .
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aij , bi . n , .
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3) , .
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x1 + x2 + + xn
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1) , , , .. * .
2) RgA = RgA*, , . , , .
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A =
~ . RgA = 2.
A* = RgA* = 3.
.
. .
= ; = 2 + 12 = 14 ¹ 0; RgA = 2;
A* =
RgA* = 2.
. : x1 = 1; x2 =1/2.
.
( (1777-1855) )
, . .
:
1 a11 ¹ 0, :
1) 21
2) 31
..
:
, d1j = a1j/a11, j = 2, 3, , n+1.
dij = aij ai1d1j i = 2, 3, , n; j = 2, 3, , n+1.
, ..
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* =
, :
, : x3 = 2; x2 = 5; x1 = 1.
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, :
, : z = 3; y = 2; x = 1.
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: {1, 2, 3, 4}.
, 3- 4 . . .
:
.
: Maple (Ó Waterloo Maple Inc.) , MapleV Release 4.
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1) + = + - .
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3) + =
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5) (a×b) = a(b )
6) (a+b) = a + b -
7) a( + ) = a + a
8) 1× =
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3) .
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, .
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D1 =
;
D2 =
D3 =
, , , : { -1/4, 7/4, 5/2}.
, , .. , , , .
:
Enter.
: Maple (Ó Waterloo Maple Inc.) , MapleV Release 4.
. (1, y1, z1), B(x2, y2, z2), .
(, , z) l/m, , :
:
x = (x1 + x2)/2; y = (y1 + y2)/2; z = (z1 + z2)/2.
.