Archivo de septiembre, 2010


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Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Sistemas para resolver

Resuelvan los siguientes sistemas de ecuaciones utilizando algunos de los métodos estudiados:
  1. \left\{\begin{array}{ccc}2x+5y+3z=10\\-2x-3y+2z=-3\\5x+3y-4z=4\end{array}\right.
    -
  2. \left\{\begin{array}{ccc}2x+5y+3z=6\\-2x-3y+2z=-9\\5x+3y-4z=17\end{array}\right.
    -
  3. \left\{\begin{array}{ccc}3x+4y-5z=6\\-2x-2y+5z=-1\\5x+4y+7z=20\end{array}\right.
    -
  4. \left\{\begin{array}{ccc}3x+2y-z=0\\5x-7y+6z=5\\3x-2y+4z=6\end{array}\right.
    -
  5. \left\{\begin{array}{ccc}x+2y+z=5\\3x-z+5z=12\\2x+4y+2z=8\end{array}\right.
    -
  6. \left\{\begin{array}{ccc}-2a+7b-3c=8\\2a-3b+11c=-12\\-5a+2b-4c=1\end{array}\right.
Clasifiquen los siguientes sistemas:
  1. \left\{\begin{array}{ccc}3x+y-2z=0\\-9x-3y+3z=6\\3x+y-z=2\end{array}\right.
    -
  2. \left\{\begin{array}{ccc}x+y+z=1\\2x-3y+z=13\\2x+2y+2z=3\end{array}\right.
    -
  3. \left\{\begin{array}{ccc}a+b-2c=2\\-a+2b+3c=5\\a+b-2c=3\end{array}\right.
    -
  4. \left\{\begin{array}{ccc}a+b-2c=-2\\-a+2b+3c=3\\a+3b+c=1\end{array}\right.
Para repasar, resuelvan los sistemas y escriban sus soluciones en los comentarios.

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deter

Determinante 3×3

¿Cómo hallar el determinante de una matriz de orden 3×3?

Es decir, como hallar el determinante de una matriz de tres filas por tres columnas.

\left\vert\begin{array}{ccc}a & b &c\\d & e & f\\g & h & j\end{array}\right\vert

Para ello debemos hacer seis multiplicaciones y sumarlas o restarlas de acuerdo al siguiente esquema.

\left\vert\begin{array}{ccc}a & b &c\\d & e & f\\g & h & i\end{array}\right\vert=a.e.i+d.h.c+b.f.g-c.e.g-h.f.a-b.d.i

Una ayuda para acordarse como armar las multiplicaciones puede ser la siguiente, las tres multiplicaciones que suma pueden obtener de las diagonales de cada color:

y las tres que restan de las siguientes diagonales:

Ejemplo:

\left\vert\begin{array}{ccc}4 & 2 &2\\-1 & 3 &5f\\1 & -1 & -2\end{array}\right\vert=4.3.(-2)+d.h.c+b.f.g-c.e.g-h.f.a-b.d.i

Pueden ver el siguiente video explicativo. Video

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Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815

Warning: Creating default object from empty value in /home/roberprof/roberprof.com/wp-includes/comment-template.php on line 815