Download PDF by the late J. G. Semple, G. T. Kneebone: Algebraic projective geometry

By the late J. G. Semple, G. T. Kneebone

ISBN-10: 0198503636

ISBN-13: 9780198503637

First released in 1952, this e-book has confirmed a worthy advent for generations of scholars. It presents a transparent and systematic improvement of projective geometry, development on thoughts from linear algebra.

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X1 − 3x2 + 5x3 − 2x4 = 0 = −4 x2 + 8x3 2x3 = 3 x4 = 1 2. La matriz aumentada de un sistema lineal ha sido transformada mediante operaciones de fila a la forma que se presenta a continuación. Determine si el sistema es consistente. ⎡ ⎤ 1 5 2 −6 ⎣0 4 −7 2⎦ 0 0 5 0 3. ¿Es (3, 4, −2) una solución del siguiente sistema? 5x1 − x2 + 2x3 = 7 −2x1 + 6x2 + 9x3 = 0 −7x1 + 5x2 − 3x3 = −7 4. ¿Para cuáles valores de h y k es consistente el siguiente sistema? 2x1 − x2 = h −6x1 + 3x2 = k 01 Maq. Cap. 1 E JERCICIOS Resuelva los sistemas de los ejercicios 1 a 4 usando las operaciones elementales de fila sobre las ecuaciones o sobre la matriz aumentada.

0 0 0 0 1 0 0 1 1 ⎤ ⎡ 1 0 0 0 ⎢0 1 1 0⎥ ⎥ c. ⎢ ⎣0 0 0 0⎦ 0 0 0 1 ⎤ ⎡ 1 1 0 1 1 ⎢0 2 0 2 2⎥ ⎥ d. ⎢ ⎣0 0 0 3 3⎦ 0 0 0 0 4 ⎤ ⎤ ⎡ ⎡ 1 1 0 0 1 1 0 1 1 1 0⎦ 0 1 1⎦ b. ⎣ 0 2. a. ⎣ 0 0 0 1 1 0 0 0 0 ⎤ ⎡ 1 0 0 0 ⎢1 1 0 0⎥ ⎥ ⎢ c. ⎣ 0 1 1 0⎦ 0 0 1 1 ⎤ ⎡ 0 1 1 1 1 ⎢0 0 2 2 2⎥ ⎥ d. ⎢ ⎣0 0 0 0 3⎦ 0 0 0 0 0 Reduzca por filas las matrices de los ejercicios 3 y 4 a la forma escalonada reducida. Encierre las posiciones pivote incluidas en la matriz final y en la matriz original, y enumere las columnas pivote. ⎤ ⎤ ⎡ ⎡ 1 3 5 7 1 2 3 4 5 7 9⎦ 5 6 7⎦ 4.

La flecha −2 2/3 para 2u tiene el doble de largo que la empleada para u, y ambas apuntan en la misma dirección. La flecha para − 23 u es dos tercios del largo de la flecha para u, y las dos apuntan en direcciones opuestas. En general, la longitud de la flecha para cu es |c| veces la Solución Vea la figura 5, donde se muestran u, 2u = 01 Maq. Cap. 3 Ecuaciones vectoriales 31 longitud de la flecha √ para u. [Recuerde que la longitud del segmento de recta desde (0, 0) hasta (a, b) es a 2 + b2 . ] ❙❙❙❙❘❙❙❙❙❚ x2 x2 – –2 u 3 0u x1 x1 u u 2u Múltiplos típicos de u El conjunto de todos los múltiplos de u FIGURA 5 Vectores en R3 x3 Los vectores en R3 son matrices columna de 3 × 1 con tres entradas.

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Algebraic projective geometry by the late J. G. Semple, G. T. Kneebone


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