Embed Size (px)
Citation preview
> >
> >
(2)(2)
> >
(3)(3)
> >
(1)(1)
Ejercicios Numero 1. Dadas las siguientes matrices:with LinearAlgebra ;
&x, Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix, BidiagonalForm,BilinearForm, CARE, CharacteristicMatrix, CharacteristicPolynomial, Column,ColumnDimension, ColumnOperation, ColumnSpace, CompanionMatrix,ConditionNumber, ConstantMatrix, ConstantVector, Copy, CreatePermutation,CrossProduct, DARE, DeleteColumn, DeleteRow, Determinant, Diagonal, DiagonalMatrix,Dimension, Dimensions, DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors,Equal, ForwardSubstitute, FrobeniusForm, GaussianElimination, GenerateEquations,GenerateMatrix, Generic, GetResultDataType, GetResultShape, GivensRotationMatrix,GramSchmidt, HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm,HilbertMatrix, HouseholderMatrix, IdentityMatrix, IntersectionBasis, IsDefinite,IsOrthogonal, IsSimilar, IsUnitary, JordanBlockMatrix, JordanForm, KroneckerProduct,LA_Main, LUDecomposition, LeastSquares, LinearSolve, LyapunovSolve, Map, Map2,MatrixAdd, MatrixExponential, MatrixFunction, MatrixInverse, MatrixMatrixMultiply,MatrixNorm, MatrixPower, MatrixScalarMultiply, MatrixVectorMultiply,MinimalPolynomial, Minor, Modular, Multiply, NoUserValue, Norm, Normalize,NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm, QRDecomposition,RandomMatrix, RandomVector, Rank, RationalCanonicalForm, ReducedRowEchelonForm,Row, RowDimension, RowOperation, RowSpace, ScalarMatrix, ScalarMultiply,ScalarVector, SchurForm, SingularValues, SmithForm, StronglyConnectedBlocks,SubMatrix, SubVector, SumBasis, SylvesterMatrix, SylvesterSolve, ToeplitzMatrix, Trace,Transpose, TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd, VectorAngle,VectorMatrixMultiply, VectorNorm, VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip
A d
1 K2 1
2 4 1
3 K2 5
A :=
1 K2 1
2 4 1
3 K2 5
B d
1 9 K1
5 8 K2
6 4 K1
B :=
1 9 K1
5 8 K2
6 4 K1
(9)(9)
> >
(5)(5)
(4)(4)
> >
> >
> >
(8)(8)
> >
(6)(6)
(7)(7)
> >
> >
> >
> >
C d
1 2 1
0 0 4
1 3 7
C :=
1 2 1
0 0 4
1 3 7
Realizar las siguientes operaciones:ACBCC
3 9 1
7 12 3
10 5 11
AKBC2. C
2. K7. 4.
K3. K4. 11.
K1. 0. 20.
A.B
K3 K3 2
28 54 K11
23 31 K4
A.CK3. C
K1. K1. K3.
3. 7. 13.
5. 12. 9.
A^3C2. A
K10. K60. 10.
70. 0. 80.
50. K180. 130.
Ejercicio Numero 2. Dadas las siguientes matrices calcule su determinante y su matriz inversa en caso de ser posible
(11)(11)
(12)(12)
(13)(13)
> >
> >
> >
> >
> >
(10)(10)
> >
> >
A d
1 K1 2 3
0 1 0 4
2 0 6 3
5 2 1 2
A :=
1 K1 2 3
0 1 0 4
2 0 6 3
5 2 1 2
Student LinearAlgebra InverseTutor A ;A^ K1
39181
K33
181K
19181
36181
K112181
53181
36181
8181
K27
181K
5181
41181
K11
181
28181
32181
K9
181K
2181
B d
1 2 1
2 1 0
1 3 1
B :=
1 2 1
2 1 0
1 3 1
Student LinearAlgebra InverseTutor B ;B^ K1
12
12
K12
K1 0 1
52
K12
K32
d d
1 2 1 3
0 1 0 4
2 0 0 0
1 0 1 2
(15)(15)
> >
(19)(19)
> >
(17)(17)
(16)(16)
> >
> >
(18)(18)
> >
> >
(14)(14)
> >
> >
d :=
1 2 1 3
0 1 0 4
2 0 0 0
1 0 1 2
Student LinearAlgebra InverseTutor d ;d^ K1
0 012
0
47
K17
0 K47
27
K47
K12
57
K17
27
017
E dK1 2
2 3
E :=K1 2
2 3
Student LinearAlgebra InverseTutor E ;E^ K1
K37
27
27
17
K d
2 2 2
2 K1 3
4 5 K10
K :=
2 2 2
2 K1 3
4 5 K10
Student LinearAlgebra InverseTutor K ;K^ K1
> >
> >
(22)(22)
(19)(19)
> >
> >
> >
(21)(21)
> >
(20)(20)
> >
> >
K5
821541
441
1641
K1441
K1
41
741
K1
41K
341
T d
1 1 1
1 2 3
1 2 4
T :=
1 1 1
1 2 3
1 2 4
Student LinearAlgebra InverseTutor T ;T^ K1
2 K2 1
K1 3 K2
0 K1 1
Ejercicio numero 3. resolver las siguietes ecuaciones lineales
A d
2 K3 1 K2 6
2 5 K2 1 3
K1 1 K2 3 K1
K3 K4 3 K3 0
A :=
2 K3 1 K2 6
2 5 K2 1 3
K1 1 K2 3 K1
K3 K4 3 K3 0
Student LinearAlgebra LinearSolveTutor A ;
2 -3 1 -2 6
2 5 -2 1 3
-1 1 -2 3 -1
-3 -4 3 -3 0
/
1-32
12
-1 3
2 5 -2 1 3
-1 1 -2 3 -1
-3 -4 3 -3 0
/
1-32
12
-1 3
0 8 -3 3 -3
-1 1 -2 3 -1
-3 -4 3 -3 0
/
1-32
12
-1 3
0 8 -3 3 -3
0-12
-32
2 2
-3 -4 3 -3 0
/
1-32
12
-1 3
0 8 -3 3 -3
0-12
-32
2 2
0-172
92
-6 9
/
1-32
12
-1 3
0 1-38
38
-38
0-12
-32
2 2
0-172
92
-6 9
/
1 0-116
-716
3916
0 1-38
38
-38
0-12
-32
2 2
0-172
92
-6 9
/
1 0-116
-716
3916
0 1-38
38
-38
0 0-2716
3516
2916
0-172
92
-6 9
/
1 0-116
-716
3916
0 1-38
38
-38
0 0-2716
3516
2916
0 02116
-4516
9316
/
1 0-116
-716
3916
0 1-38
38
-38
0 0 1-3527
-2927
0 02116
-4516
9316
/
1 0 0-1427
6427
0 1-38
38
-38
0 0 1-3527
-2927
0 02116
-4516
9316
/
1 0 0-1427
6427
0 1 0-19
-79
0 0 1-3527
-2927
0 02116
-4516
9316
/
1 0 0-1427
6427
0 1 0-19
-79
0 0 1-3527
-2927
0 0 0-109
659
/
1 0 0-1427
6427
0 1 0-19
-79
0 0 1-3527
-2927
0 0 0 1-132
/
(23)(23)
> >
> >
> >
> >
1 0 0 0 -1
0 1 0-19
-79
0 0 1-3527
-2927
0 0 0 1-132
/
1 0 0 0 -1
0 1 0 0-32
0 0 1-3527
-2927
0 0 0 1-132
/
1 0 0 0 -1
0 1 0 0-32
0 0 1 0-192
0 0 0 1-132
X=-1, Y=-3/2, Z= -19/2, T= -13/2
B d
1 1 K2 4
2 K1 4 4
2 K1 6 K1
B :=
1 1 K2 4
2 K1 4 4
2 K1 6 K1
Student LinearAlgebra LinearSolveTutor B ;
1 1 -2 4
2 -1 4 4
2 -1 6 -1
/
1 1 -2 4
0 -3 8 -4
2 -1 6 -1
/
1 1 -2 4
0 -3 8 -4
0 -3 10 -9
/
1 1 -2 4
0 1-83
43
0 -3 10 -9
/
1 023
83
0 1-83
43
0 -3 10 -9
/
1 023
83
0 1-83
43
0 0 2 -5
/
1 023
83
0 1-83
43
0 0 1-52
/
1 0 0133
0 1-83
43
0 0 1-52
/
> >
(24)(24)
> >
> >
> >
> >
1 0 0133
0 1 0-163
0 0 1-52
X = 6, Y =K2, Z =K52
C d
2 4 6 18
4 5 6 24
2 7 12 30
C :=
2 4 6 18
4 5 6 24
2 7 12 30
Student LinearAlgebra LinearSolveTutor C ;
2 4 6 18
4 5 6 24
2 7 12 30
/
1 2 3 9
4 5 6 24
2 7 12 30
/
1 2 3 9
0 -3 -6 -12
2 7 12 30
/
1 2 3 9
0 -3 -6 -12
0 3 6 12
/
1 2 3 9
0 1 2 4
0 3 6 12
/
1 0 -1 1
0 1 2 4
0 3 6 12
/
> >
(28)(28)
> >
> >
> >
> >
> >
(27)(27)
> >
> >
> >
(26)(26)
> > (29)(29)
> >
(25)(25)
1 0 -1 1
0 1 2 4
0 0 0 0
el sistema tiene infinita soluciones, es decir, es inconsistente indetermindo
Ejercicio numero 4. dadas estas matrices , comprobr que det A .det B = det Ab
A d
1 3 1 2
0 K1 3 4
2 1 9 6
4 2 4 2
; B d
2 0 2 1
0 1 6 2
0 0 1 2
1 2 3 0
A :=
1 3 1 2
0 K1 3 4
2 1 9 6
4 2 4 2
B :=
2 0 2 1
0 1 6 2
0 0 1 2
1 2 3 0
Det A Det B = Det AB ;
Det
1 3 1 2
0 K1 3 4
2 1 9 6
4 2 4 2
Det
2 0 2 1
0 1 6 2
0 0 1 2
1 2 3 0
= Det AB
Determinant A Determinant B ;5332
Det A.B ;
Det
4 7 27 9
4 7 9 4
10 13 37 22
10 6 30 16
Determinant A.B ;5332
