Matrices
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ÍNDICE
CONTENIDO……………………………………………………………...…….11 CONTENIDO……………………………………………………………...…….
TEMA…………………………………………………………………………....2
OBJETIVOS…………………………………………………………………….. OBJETIVOS……………………………………………………………………..22
OBJETIVO GENERAL………………………………………………………...2 GENERAL………………………………………………………...2
OBJETIVOS ESPECÍFICOS…………………………………………………....2 ESPECÍFICOS…………………………………………………....2
JUSTIFICACIÓN………………………………………………………………..22 JUSTIFICACIÓN………………………………………………………………..
MARCO TEÓRICO……………………………………………………………..3 TEÓRICO……………………………………………………………..3
DESARROLLO………………………………………………………………...14 DESARROLLO……………………………………………………………… ...14
CONCLUSIONES………………………………………………………….......28 CONCLUSIONES………………………………………………………… .......28
RECOMENDACIONES……………………………………………………….299 RECOMENDACIONES……………………………………………………….2
BIBLIOGRAFÍA………………………………………………………………3 BIBLIOGRAFÍA………………………………………………………………300
1
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1. TEMA
Diseño de un software en entorno Visual Basic 2010 sobre matrices
2. OBJETIVOS 2.1. OBJETIVO GENERAL
Crear una aplicación sobre Matrices en Visual Basic donde podamos realizar varias operaciones.
2.2. OBJETIVOS ESPECÍFICOS ESPECÍFICOS
Investigar el funcionamiento de los diferentes comandos que posee el lenguaje de programación Visual Visual Basic, para así así lograr un correcto correcto manejo del mismo. mismo. Indagar métodos y estrategias que nos ayuden a la programación para así lograr el correcto funcionamiento del mismo. Verificar la importancia que tiene las matemáticas y mediante los conocimientos adquiridos ponerlos en práctica práctica y crear un programa que ayude ayude a desarrollar operaciones operaciones con matrices. matrices. Desarrollar operaciones dentro del programa como: suma, resta, suma de diagonales, producto entre matices, escalar por matriz, inversa, transpuesta, determinante.
3. JUSTIFICACIÓN
Debido a la falta de preocupación y desempeño de los estudiantes se propone crear una aplicación en Visual Basic, cuya función principal consistirá en resolver operaciones básicas con matrices.
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eficaz. Por otra parte, los resultados del estudio contribuirán a que el personal docente tenga una herramienta herramienta de trabajo que que cumpla con con sus expectativas y traiga satisfacción satisfacción en los mismos. El proyecto es factible realizarse ya que se posee conocimientos de trabajos similares realizados anteriormente, además se cuenta con el apoyo de profesores, personal del departamento y se dispone de la infraestructura adecuada para el desarrollo del mismo.
4. MARCO TEÓRICO 4.1. VISUAL BASIC Visual Basic es un un lenguaje de programación programación dirigido por eventos, eventos, desarrollado por Alan Alan Cooper para Cooper para Microsoft. Microsoft. Este lenguaje de programación es un dialecto de BASIC, BASIC, con importantes agregados. Su primera versión fue presentada en 1991, 1991, con la intención de simplificar la programación utilizando un ambiente un ambiente de desarrollo que facilitó en cierta medida la programación la programación misma. La última versión fue la 6, liberada en 1998, para la que Microsoft extendió el soporte hasta marzo de 2008. En 2001 Microsoft propuso abandonar el desarrollo basado en la API Win32 API Win32yy pasar a un framework un framework o marco común de librerías, independiente de la versión del sistema operativo, .NET Framework, Framework, a través de Visual Basic .NET (y otros lenguajes como C como C Sharp (C#) de fácil transición de código entre ellos); fue el sucesor de Visual Basic 6. Aunque Visual Basic es de propósito general, también provee facilidades para el desarrollo de aplicaciones de bases de bases de datos usando Data usando Data Access Objects, Remote Objects, Remote Data Objects o ActiveX Data Objects. Visual Basic contiene un entorno de desarrollo integrado o IDE que integr aeditor aeditor de textos para textos para edición del código fuente, un depurador, un depurador, uncompilador uncompilador (y enlazador) (y enlazador) y y un editor de interfaces gráficas o GUI. o GUI. Índice
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4.1.1. HISTORIA Todas las versiones de Visual Basic para Windows son muy conocidas, aunque la Microsoft Visual Basic 1.0 desarrollada para el sistema operativo MS-DOS (ediciones Profesional y Estándar), que data de 1992, fue menos difundida. Esta proveía un entorno que, aunque en modo texto, incluía un diseñador de formularios en el que se podían arrastrar y soltar distintos controles. La última versión que sólo generaba aplicaciones de 16 bits fue la 3.0, y no incluía una biblioteca detallada de componentes para toda clase de usos. Durante la transición de los sistemas Windows sistemas Windows 3.11 a Windows 95, en 95, en 1995, hizo su aparición la versión 4.0 de Visual Basic; ésta podía generar programas tanto de 16 como de 32 bits, a partir del mismo código fuente, aunque a costa de un gran aumento en el tamaño de los archivos necesarios en tiempo de ejecución ("runtime"). Además, se sustituyeron los controles denominados VBX por los nuevos OCX. nuevos OCX. Con Con la siguiente versión, la 5.0, se estuvo a punto de implementar por primera vez la posibilidad de compilar a código nativo, obteniendo una mejora de rendimiento considerable. Tanto esa como la sucesora 6.0 soportaban ciertas características propias de los lenguajes los lenguajes orientados a objetos, pero objetos, pero carecían de algunas importantes, tales como herencia y sobrecarga; pero, de hecho, no fue pensado como lenguaje orientado a objetos. La versión 6.0, que puede generar código ejecutable directo en 32 bits, continúa aún utilizándose masivamente, y es compatible con las últimas versiones de los sistemas Windows, como Windows 7 y Windows 8. Visual Basic evolucionó para integrar la plataforma .NET; .NET; allí perdió su propia identidad como lenguaje único adquirible, pasando a integrar un paquete de productos, llamado precisamente Microsoft .NET; dentro de ese paquete o framework se encuentra el nuevo y llamado Visual llamado Visual Basic .NET, que .NET, que trabaja sobre el entorno Microsoft entorno Microsoft Visual Studio. Esta Studio. Esta nueva versión del lenguaje posee profundas diferencias en la forma de programar respecto de Visual Basic 6, pero gran semejanza en su sintaxis básica. Cabe mencionar que, aunque fue menos conocido, se desarrolló también una versión gratuita de Visual Basic 5.0, orientada al desarrollo de controles y componentes; su nombre específico era Microsoft Visual Basic 5.0 Control Creation Edition (Visual Basic 5 CCE). También hubo
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4.1.2. VERSIONES Visual Basic 1.0 para Windows se liberó en mayo de 1991. Visual Basic 1.0 para MS-DOS para MS-DOS fue liberada en septiembre de 1992. de 1992. Poco popular, este lenguaje no era compatible con Visual Basic para Windows, ya que constituía en realidad la siguiente
versión
de
los
compiladores
BASIC
vigentes
para
DOS,
denominados QuickBASIC denominados QuickBASIC y BASIC PDS (Profesional Development System). Usaba una interfaz de texto, con caracteres ASCII extendidos que daban la apariencia de una interfaz gráfica. Visual Basic 2.0 fue liberado en noviembre de 1992. 1992. Venía en versiones Standard y Professional. El entorno de programación era más fácil de usar que el anterior, y su velocidad de proceso fue mejorada. En particular, los formularios se convirtieron en objetos instanciables, sentando así los conceptos fundamentales para módulos de clase, que más tarde se ofrecerían en la versión 4. Visual Basic 3.0 salió al mercado en verano de 1993, en 1993, en versiones Standard y Profesional. Incluía la versión 1.1 de Microsoft Jet Database Engine, que permitía acceso a bases de datos Access. datos Access. Visual Basic 4.0, surgida en agosto de 1995, de 1995, fue fue la primera versión que generaba aplicaciones aplicaciones tanto de 16 como de 32 bits 32 bits para para Windows. Había incompatibilidades entre las distintas realeases de esta versión que causaban fallas de instalación y problemas de operación. Mientras las anteriores utilizaban controles VBX, con la 4.0 se comenzaron a utilizar controles OLE controles OLE en archivos OCX, archivos OCX, que que más tarde se llamarían controles ActiveX. controles ActiveX. En febrero de 1997, de 1997, Microsoft Microsoft lanzó Visual Basic 5.0, versión que generaba programas de 32 bits exclusivamente. exclusivamente. Losprogramadores Losprogramadores que aún preferían desarrollar aplicaciones en 16 bits debían necesariamente utilizar VB 4.0, siendo transportables en código fuente a VB 5.0 y viceversa. En la versión 5 se tenía la posibilidad de crear controles personalizados; también permitía compilar a código ejecutable nativo de Windows, logrando con ello incrementar la velocidad de ejecución de los programas generados, más notablemente en los de cálculo. Visual Basic 6.0, salido a mediados de 1998, 1998, muy mejorado, incrementó el número de
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compatibles con plataformas más modernas, como Windows Vista, Windows Server 2008,Windows 2008 ,Windows 7 y Windows 8. 8 .2 3 El soporte estándar para Microsoft Visual Basic 6.0 finalizó el 31 de marzo de 2005, pero el extendido terminó en marzo de 2008. 2008 .4 La comunidad de usuarios de Visual Basic expresó su grave preocupación y se firmó una petición para mantener el producto vivo .5 Microsoft se ha negado hasta el momento a cambiar su posición sobre el asunto. Irónicamente, en esa época (2005) se da a conocer que el software antiespía ofrecido por Microsoft, "Microsoft AntiSpyware" (parte de la GIANT Company Software), fue codificado en Visual Basic 6.0; su posterior sustituto, Windows Defender, fue reescrito en código C++. C++ .6
4.1.3. CARACTERISTICAS Los compiladores de Visual Basic generan código que requiere una o más librerías de enlace dinámico para que funcione, conocidas comúnmente como DLL (sigla en inglés de dynamiclink library); en algunos casos reside en el archivo llamado MSVBVMxy.DLL (siglas de "MicroSoft Visual Basic Virtual Machine x.y", donde x.y es la versión) y en otros en VBRUNXXX.DLL ("Visual Basic Runtime X.XX"). Estas bibliotecas DLL proveen las funciones básicas implementadas en el lenguaje, conteniendo rutinas en código ejecutable que son cargadas bajo demanda en tiempo de ejecución. Además de las esenciales, existe un gran número de bibliotecas del tipo DLL con variedad de funciones, tales como las que facilitan el acceso a la mayoría de las funciones del sistema operativo o las que proveen medios para la integración con otras aplicaciones. Dentro del mismo Entorno mismo Entorno de desarrollo integrado (IDE) de Visual Basic se puede ejecutar el programa que esté desarrollándose, es decir en modo intérprete modo intérprete (en realidad pseudo-compila el programa muy rápidamente y luego lo ejecuta, simulando la función de un intérprete puro). Desde ese entorno también se puede generar el archivo en código ejecutable (exe); (exe); ese programa así generado en disco puede luego ser ejecutado sin requerir del ambiente de programación (incluso en modo stand modo stand alone), alone), aunque sí será necesario que las librerías DLL requeridas por la aplicación desarrollada se encuentren también instaladas en el sistema para sistema para posibilitar su ejecución. ejecución. El propio Visual Basic provee soporte para empaquetado y distribución; distribución; es decir, permite
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Así como bibliotecas DLL, hay numerosas aplicaciones desarrolladas por terceros que permiten disponer de variadas y múltiples funciones, incluso mejoras para el propio Visual Basic; las hay también para el empaquetado y distribución, y hasta para otorgar mayor funcionalidad al entorno de programación (IDE).
4.1.4. ENTORNO DE DESARROLLO Existe un único entorno de desarrollo para Visual Basic, desarrollado por Microsoft: Microsoft Visual Basic x.0, correspondientes a versiones desde la 1.0 hasta la 6.0, (con respectivas diferencias entre versiones del lenguaje). El entorno de desarrollo es muy similar al de otros lenguajes. Realizando una instalación típica del producto, las características básicas se presentan de la siguiente forma: En la parte superior aparecen tres elementos, en este orden: la barra de título donde figura el nombre del proyecto en curso y su estado (diseño o ejecución); la barra de menú con 13 opciones desplegables y una barra de herramientas ; esta última se puede personalizar, posibilitando la inclusión inclusión de prácticamente prácticamente la totalidad de los comandos del IDE. En la parte central, cubriendo la franja de mayor área, se encuentra el espacio de trabajo. Éste incluye y muestra las ventanas del proyecto, las vistas del código del código fuente de los módulos, los objetos y los controles que contienen las ventanas de la l a aplicación y el panel de controles. El panel de controles, que aunque es móvil normalmente está ubicado a la derecha, por defecto cuenta con los siguientes controles: PictureBox: Caja de imágenes i mágenes Label: Etiqueta Label: Etiqueta
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HScrollBar: Barra de desplazamiento horizontal VScrollBar: Barra de desplazamiento vertical Timer: Temporizador Timer: Temporizador DriveListBox: Lista de unidades de disco DirListBox: Lista de directorios FileListBox: Lista de archivos Shape: Figura Line: Línea Image: Imagen Data: Conexión a origen de datos OLE: Contenedor de documentos embebidos compatibles con Object Linking and Embedding Además de los listados, se pueden agregar todo tipo de controles de terceros, y hay una gran cantidad de ellos que se proveen con el propio Visual Basic 6.0. Los controles vienen embebidos dentro de archivos con extensión OCX. extensión OCX. Las ventanas de proyecto, aunque móviles, se encuentran en el panel lateral derecho y contienen dos vistas principales: El Explorador de proyectos, que muestra todos los elementos que componen el proyecto o grupos de proyectos (formularios, interfaz de controles, módulos de código, módulos de clase, etc.)
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Es uno de los lenguajes de uso más extendido, por lo que resulta fácil encontrar información, documentación documentación y fuentes para los proyectos. Fácilmente extensible mediante librerías DLL y componentes ActiveX de otros lenguajes. Posibilita añadir soporte para ejecución de scripts, VBScript o JScript, en las aplicaciones mediante Microsoft mediante Microsoft Script Control. Tiene acceso a la API la API multimedia de DirectX (versiones 7 y 8). También está disponible, de forma no oficial, un componente para trabajar con OpenGL 1.1. 1.1 .7 Existe una versión, VBA, versión, VBA, integrada integrada en las aplicaciones de Microsoft de Microsoft Office, tanto Office, tanto Windows como Mac, que permite programar macros para extender y automatizar funcionalidades en documentos, hojas de cálculo y bases de datos (Access). (Access). Si bien permite desarrollar grandes y complejas aplicaciones, también provee un entorno adecuado para realizar pequeños prototipos rápidos.
4.2. MATRICES 4.2.1 DEFINICION La definición de matriz aparece por primera vez en el año 1850, introducida por J. J. Sylvester. Sin embargo, embargo, hace más de dos mil años los matemáticos matemáticos chinos habían escubierto ya un método de resolución de sistemas deecuaciones lineales y, por lo tanto, empleaban tablas con números. El desarrollo inicial de la teoría de matrices se debe al matemático W. R.Hamilton, en 1853. En 1858, Arthur Cayley introduce la notación matricial como una forma abreviada de escribir un sistema de m ecuaciones lineales con n incógnitas, la misma que fue descrita en su
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temas que se analizarán en cursos superiores de cálculo. Además de su utilidad util idad para el estudio de sistemas de ecuaciones, las matrices aparecen de forma natural en informática, geometría, estadística, economía, física, logística, etc. La utilización de matrices constituye actualmente una parte esencial de los lenguajes de programación, ya que la mayoría de los datos se introducen i ntroducen en las computadoras como tablas organizadas en filas y columnas: hojas de cálculo, bases de datos, entre otros. Una matriz real A es un arreglo rectangular de números reales, en donde cada elemento aij que pertenece a la matriz A tiene dos subíndices. El subíndice i representa la fila (disposición horizontal), y el subíndice j representa la columna (disposición vertical), en las cuales se encuentra el elemento. FOTO MATRIZ Si la matriz A tiene m filas y n columnas, se dice que es de dimensión u orden m x n y se denota como: Amxn. Se usará ∀ i ∀ j para denotar 1 ≤ i ≤ m, 1 ≤ j ≤ n. Las matrices se denotan con letras mayúsculas: A, B, C ... ... y los elementos de las mismas con letras minúsculas y subíndices que indican el lugar que ocupan: aij, bij, cij, ... Se puede utilizar el paréntesis curvo o recto para dibujar en su parte interior cada uno de sus elementos. 4.2.2.
OPERACIONES CON MATRICES
4.2.2.1. SUMA
Dadas dos matrices Amxn y Bmxn del mismo orden, se define la suma de matrices como una nueva matriz Cmxn del mismo orden, C = A + B, tal que: ∀ i∀ j(cij = aij + bij.
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4.2.2.2. MULTIPLICACIÓN MULTIPLICACIÓN DE UNA MATRIZ MATRIZ POR UN ESCALAR ESCALAR Dado un escalar λ y una matriz Amxn, se define la multiplicación de una matriz por un escalar como una nueva matriz Bmxn, B =λ A, tal que: ∀ i∀ j(bij = λaij). Es decir, cada elemento de la matriz B es obtenido multiplicando el escalar λ por cada elemento de la matriz A. Sea el conjunto de matrices de orden m x n, la multiplicación de una matriz por un escalar cumple con las siguientes si guientes propiedades: propiedades:
4.2.2.3.
MULTIPLICACIÓN ENTRE MATRICES
Dadas dos matrices Amxn y Bnx p, se define la multiplicación entre matrices como una nueva matriz Cmx p, C = AB, tal que: ∀ i∀ j
(cij = ai1b1 j + ai2b2 j +
+ ainbnj).
Es decir, cada elemento de la matriz producto C es obtenido sumando los productos de cada elemento de la fila i de la matriz A por el correspondiente elemento de la columna j de la matriz B. De aquí que, es importante que el número de columnas de la matriz localizada a la
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Se puede verificar que:
La multiplicación entre matrices no es conmutativa, esto es, AB ≠ BA. AB = 0, aunque A y B no sean matrices nulas
La potencia An para matrices cuadradas, cuadradas, representa representa la multiplicación n veces de la misma matriz A.
Una matriz es idempotente si A2 = A.
p ∈ Una matriz es periódica de período p si Ap = A ( p
Una matriz es involutiva si A2 = I .
p ∈ Una matriz es nilpotente de índice p si Ap = 0 ( p
∧
∧
p>1).
p>1).
Para utilizar la propiedad distributiva se requiere que la matriz común esté multiplicando a las demás por la misma ubicación (izquierda o derecha). Así, B + C ) o como ( B B + C ) A A. dada AB + CA, no es posible expresarla como A( B
4.2.2.3. TRANSPOSICIÓN DE UNA MATRIZ Dada una matriz A de orden m×n, para obtener la matriz transpuesta, la cual se denota por AT , se deben intercambiar los elementos de las filas por las columnas. Note que la nueva matriz AT es de orden n×m.
Sea el conjunto de matrices de orden m×n , la transposición cumple con las siguientes propiedades: propiedades:
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Propiedades Propiedades de la Matriz Inversa Para obtener la inversa de una matriz, se puede utilizar el método de Gauss- Jordan o el de la matriz de cofactores transpuesta. El objetivo del método de Gauss-Jordan es transformar la matriz A por medio de operaciones algebraicas entre renglones en la matriz identidad I equivalente y simultáneamente la identidad I en la inversa de A. Para tal efecto, las operaciones que están permitidas son:
Multiplicar una fila por una constante k diferente de cero.
Intercambiar dos filas.
Sumar un múltiplo de una fila a otra.
4.2.2.5. DETERMINANTE
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matriz 4 x 4, debe expresarse en función de determinantes de submatrices 3 x 3 utilizando los respectivos cofactores, y así sucesivamente por cada nuevo incremento.
5. DESARROLLO
Para mayor entendimiento se lo resumirá en partes p artes
5.1. FORM1 (Principal) 5.1.1 INTERFAZ USUARIO
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5.1.2. INTERFAZ PROGRAMADOR
5.2. FORM 2 (Acerca de:) 5.2.1. INTERFAZ USUARIO
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5.2.2. INTERFAZ PROGRAMADOR
5.3. FORM 3(Documento MATRICES) 5.3.1. INTERFAZ USUARIO
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5.3.2. INTERFACE PROGRAMADOR
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