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ISBN-10: 0321287134

ISBN-13: 9780321287137

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Additional resources for Álgebra Lineal y sus aplicaciones

Example text

Solución Utilice las definiciones de multiplicación escalar y suma de vectores para reescribir la ecuación vectorial ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ 1 2 7 x1⎣ −2 ⎦+ x2 ⎣ 5 ⎦ = ⎣ 4 ⎦ −5 6 −3 a1 a2 b la cual es la misma que ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ x1 2x2 7 ⎣ −2x1 ⎦ + ⎣ 5x2 ⎦ = ⎣ 4 ⎦ −5x1 6x2 −3 y ⎡ ⎤ ⎡ ⎤ x1 + 2x2 7 ⎣ −2x1 + 5x2 ⎦ = ⎣ 4 ⎦ −3 −5x1 + 6x2 (2) Los vectores que aparecen en los lados derecho e izquierdo de (2) son iguales si, y sólo si, sus entradas correspondientes son iguales. Esto es, x1 y x2 hacen que la ecuación 01 Maq.

Asimismo, como el sistema original puede producirse mediante operaciones de fila sobre el sistema nuevo, cada una de las soluciones del sistema nuevo también es una solución del sistema original. Esta explicación justifica el hecho siguiente. Si las matrices aumentadas de dos sistemas lineales son equivalentes por filas, entonces los dos sistemas tienen el mismo conjunto solución. Aunque el ejemplo 1 es extenso, puede afirmarse que, después de algún tiempo de práctica, los cálculos se ejecutan con rapidez.

Vp con pesos c1, c2, . . , cp. La propiedad (ii) enunciada anteriormente permite omitir los paréntesis cuando se forma una combinación lineal de este tipo. En una combinación lineal, los pesos pueden ser cualesquiera números reales, incluso el cero. Por ejemplo, algunas combinaciones lineales de los vectores v1 y v2 son √ 1 3v1 + v2 , v (= 12 v1 + 0v2 ), y 0 (= 0v1 + 0v2 ) 2 1 En la figura 8 se identifican algunas combinaciones lineales selecciona2 −1 . ) Estime las combinaciones lineales de v1 y v2 que generan los vectores u y w.

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Álgebra Lineal y sus aplicaciones by DAVID C. LAY

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