(3.1)
- , - , .
(3.1)
(3.2)
, .. . (3.2) .
, , , . , , , . .
, , .
:
1) ;
2) ;
3) , .
.
(3.1)
(3.2)
, , ..
(3.3)
, .
(3.1) - : , (3.1) , .
.
MatrixRank[A]
MatrixRank[B]
, .
.
, .
1. .
. , . .
.
MatrixRank[A]
MatrixRank[B]
. B .
|
|
MatrixForm[RowReduce[B]]
2. .
, , . , .
B={1.5471,1.6471,1.7471,1.8471};
.
X=Inverse[A].B
{1.04058,0.986956,0.935053,0.881297}
3. .
Mathematica .
1) , .
2) , .
.
B={1.5471,1.6471,1.7471,1.8471};
, A.
A1=Transpose[A];
.
1.04058
0.986956
0.935053
0.881297
4. .
Mathematica . .
.
A=Table[Random[],{i,1,1000},{j,1,1000}];
Do[A[[i,i]]=2,{i,1,1000}];
.
B=Table[35*Sin[i*0.01],{i,1,1000}];
.
X=Timing[LinearSolve[A,B]]
X[[1]]
0.578 Second
.
Max[Abs[A.X[[2]]-B]]
.
, .
(3.3)
, , . , , , (.. ) . , , , , .
, , , .
. , , , . .
1) .
2) .
3) .
( ) (2.2) , .
|
|
(2.2) , , , . , , . (2.2) , .
Mathematica , , .
.
MatrixRank[A]
4-2=2 . .
R=NullSpace[A]
{{-7,5,0,1},{8,-6,1,0}}
.
m=Length[R]
C1=Table[c[i],{i,1,m}];
X=C1.R
{-7 c[1]+8 c[2],5 c[1]-6 c[2],c[2],c[1]}
, , . . .
1) .
2) .
.
, ,
MatrixRank[A]
MatrixRank[B]
, . .
C1={1,-7,2,3};
X1=LinearSolve[A,C1]
.
R=NullSpace[A]
{{-1,0,0,3,0},{-2,3,0,0,0}}
m=Length[R]
C1=Table[c[n],{n,1,m}];
X=X1+C1.R
{ } - , .
{ } . .
, .. , , - .
.
.
. ,
,
.
.
. .
.
R=LinearSolve[A,B];