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Si \(AB=I\) entonces \(A\) es invertible y \(A^{-1}=B\)
Si \(AB=I\) entonces \(A\) es invertible y \(A^{-1}=B\)
Vamos a demostrar el notable teorema que dice que, dadas dos matrices cuadradras \(A\) y \(B\) del mismo tamaño, si \(AB=I\), donde \(I\) es la matriz identidad del mismo tamaño que la matrices \(A\) y \(B\), entonces \(A\) es invertible y \(B^{-1}=A\). La prueba será directa y sólo usaremos el hecho de que si \(|A|\ne0\) entonces \(A\) es invertible. La pregunta es si puedes tú, estimado estudiante, ofrecer otra prueba de la que aquí se sugiere. Sirva además este texto como un ejemplo de escritura con LaTeX.
Memo Garro
The Math Mag Article Template
The Math Mag Article Template
Downloaded from Mathematics Magazine's website. Mathematics Magazine offers lively, readable, and appealing exposition on a wide range of mathematical topics.
Mathematical Association of America
Automobile Suspension Design
Automobile Suspension Design
Vibration control is crucially important in ensuring a smooth ride for vehicle passengers. This study sought to design a suspension system for a car such that its mode of vibration would be predominantly bouncing at lower speeds, and primarily pitching at higher speeds. Our study used analytical and numerical methods to choose appropriate springs and dampers for the front and rear suspension. After an initial miscalculation, we succeeded in arriving at appropriate shocks for the vehicle with the desired modes of vibration at the specified frequencies. We then assessed the maximum bouncing and pitching that the vehicle would experience under a specific set of conditions: travel at 40 km/hr over broken, rough terrain. Our testing showed moderate success in our suspension design. We successfully damped the force being transmitted to both the front and rear quarter car somewhat, while ensuring that the modes of vibration fell into the desired shapes at the desired frequency ranges.
Little Ian
INTRODUÇÃO AO CÁLCULO DIFERENCIAL EM UMA ÚNICA VARIÁVEL: Uma visão generalizada e informal
INTRODUÇÃO AO CÁLCULO DIFERENCIAL EM UMA ÚNICA VARIÁVEL: Uma visão generalizada e informal
Um artigo que sugere somente a compreensão dos limites, sem o uso de sua definição formal, que se desenvolve até o entendimento das operações de diferenciação.
João Gabriel Bento
Generalidades de las soluciones a las ecuaciones de Einstein en presecia de una densidad del vacio que decae monotonamente con el parametro de Hubble en un espacio-tiempo plano
Generalidades de las soluciones a las ecuaciones de Einstein en presecia de una densidad del vacio que decae monotonamente con el parametro de Hubble en un espacio-tiempo plano
En este trabajo se estudia el comportamiento general del parametro de Hubble para un universo plano que alberga un gas ideal con presion positiva o nula junto con una densidad del vacio compuesta por un termino de costante cosmologica y un termino proporcional a una potencia positiva del parametro de Hubble. Al final se hace el paralelo entre un universo en expansion y el fenomeno de colapso gravitacional esfericamente simetrico. Obtenemos como conclusion que algunas dependencias de la densidad del vacio que crecen mas rapido que H2 inpiden la existencia de singularidades en procesos netamente gravitacionales.
leonardo duarte
Determining the Ratio of Specific Heats of\\ Gases using Adiabatic Oscillations
Determining the Ratio of Specific Heats of\\ Gases using Adiabatic Oscillations
The ratios of specific heats, γ = (CP/CV), for three gases (air, argon and carbon dioxide) were calculated by measuring the oscillations of different masses in various apparatus. The experiments followed Rüchardt's and Rinkel's methods; a 100ml glass gas syringe was additionally used to extend the investigation as well as a technique to elimination of friction. The approaches and results were compared; the most accurate method (Rüchardt's method alongside compensation for friction) yielded: Air, γ = 1.358 ± 0.0038 Argon, γ = 1.6597 ± 0.0009 Carbon dioxide, γ = 1.2996 ± 0.0087 These differ from the literature value by 3.0%, 0.6% and 1.5% respectively. The reasons for these apparent discrepancies are discussed.
Pip Armstrong
Homework #1 Template
Homework #1 Template
A mathematics homework template.
Amanda
Definition Homework
Definition Homework
Latex assignment of the definition of a derivative
Joshua Garrett
Homework Template
Homework Template
A homework template. Modified from Igor Shevtsov's template.
Karla Hernandez

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