, . , : ×, .
= , B = .
= +
= ,
c11 = a11 + b11, c12 = a12 + b12, cij = aij + bij, , cmn = amn + bmn.
1. , : ) = , = ; ) = , = ; ) = , = . : ) 2 × 3. : = + = . ) . : = + = . ) , .. 3×2, 2×3; . |
, , . :
1) : + = + , , ×;
2) : ( + ) + = + ( + ), , - , ×;
, , + (- ) = 0, .. , .
k kA, kaij, .. = , kA = .
.
2. = k = 3. . 3 = . 3. , = . . k = -1. - = . 4. 3 2, = , = . . k 1 = 3 k2 = -2. 3 = , -2 = . : 3 2 = . |
.
= , B = .
= = .
11 , (.. 11 12) (.. b11 b21) : c11 = a11b11 + a12b21.
, , i j -, i (i1, i2, , in) j (b1j, b2j, , bnj) B .
5. , = , = . . -: c11 = a11b11 + a12b21 + a13b31 = 31 + 12 + 11 = 6; c12 = a11b12 + a12b22 +a13b32 = 31 + 1(-1) + 10 = 2; c13 = a11b13 + a12b23 + a13b33 = 3(-1) + 11 + 11 = -1; c21 = a21b11 +a22b21 + a23b31 = 21 + 12 + 21 = 6; c22 = a21b12 + a22b22 +a23b32 = 21 + 1(-1) + 20 = 1; c23 = a21b13 +a22b23 +a23b33 = 2(-1) + 11 + 21 = 1; c31 = a31b11 + a32b21 + a33b31 = 11 + 22 + 31 = 8; c32 = a31b12 + a32b22 + a33b32 = 11 + 2(-1) + 30 = -1; c33 = a31b13 + a32b23 + a33b33 = 1(-1) + 21 + 31 = 4. , = . |
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- .
6. , = . = |
, , .
:
1) , ;
2) , , , , .
= , = . :
=
= .
, ≠. , , , .
, : () = ( , ( +) = + .
. , , , . , .. , . , = = ,
= .