2013-10-03T11:51:54Z https://matematicasies.com/Selectividad-Andalucia-2011-5-B1#comment1217 2013-10-03T11:51:54Z

<p>Otra forma de resolver el apartado b)</p> <p>Tenemos que resolver la ecuación matricial <img src='https://matematicasies.com/local/cache-TeX/440275725eaa4ea11985ee13761d99da.png' style="vertical-align:middle;" width="130" height="45" alt="A \cdot A^t \cdot X = B" title="A \cdot A^t \cdot X = B"> <br>En el apartado anterior ya hemos calculado <img src='https://matematicasies.com/local/cache-TeX/105dea8005ea2cb61f9915bd57b6175f.png' style="vertical-align:middle;" width="55" height="45" alt="A \cdot A^t" title="A \cdot A^t">, y la matriz <img src='https://matematicasies.com/local/cache-TeX/9d5ed678fe57bcca610140957afab571.png' style="vertical-align:middle;" width="22" height="40" alt="B" title="B"> nos la da el enunciado. Si sustituimos queda:</p> <p><img src='https://matematicasies.com/local/cache-TeX/ece624c1d456275be0d7385b68936f81.png' style="vertical-align:middle;" width="235" height="72" alt="\left( \begin{array}{cc} 1 & 0 \\ 0 & 2 \end{array} \right) \cdot X = \left( \begin{array}{cc} 3 & -1 \\ 1 & 2 \end{array} \right)" title="\left( \begin{array}{cc} 1 & 0 \\ 0 & 2 \end{array} \right) \cdot X = \left( \begin{array}{cc} 3 & -1 \\ 1 & 2 \end{array} \right)"></p> <p>Deducimos que la matriz <img src='https://matematicasies.com/local/cache-TeX/02129bb861061d1a052c592e2dc6b383.png' style="vertical-align:middle;" width="23" height="40" alt="X" title="X"> tiene que ser de 2x2. Por tanto la expresión quedaría:</p> <p><img src='https://matematicasies.com/local/cache-TeX/40839607d380b7ece7d4b629e4057bd2.png' style="vertical-align:middle;" width="293" height="72" alt="\left( \begin{array}{cc} 1 & 0 \\ 0 & 2 \end{array} \right) \cdot \left( \begin{array}{cc} a & b \\ c & d \end{array} \right) = \left( \begin{array}{cc} 3 & -1 \\ 1 & 2 \end{array} \right)" title="\left( \begin{array}{cc} 1 & 0 \\ 0 & 2 \end{array} \right) \cdot \left( \begin{array}{cc} a & b \\ c & d \end{array} \right) = \left( \begin{array}{cc} 3 & -1 \\ 1 & 2 \end{array} \right)"> <br>donde <img src='https://matematicasies.com/local/cache-TeX/ba9bf43ad118aadf5af90daf8adbe32e.png' style="vertical-align:middle;" width="70" height="40" alt="a, b, c, d" title="a, b, c, d"> son los elementos de la matriz <img src='https://matematicasies.com/local/cache-TeX/02129bb861061d1a052c592e2dc6b383.png' style="vertical-align:middle;" width="23" height="40" alt="X" title="X"> que queremos calcular. <br>Hacemos el producto de matrices en el lado izquierdo del signo igual</p> <p><img src='https://matematicasies.com/local/cache-TeX/d76e906d856cd9bca3ad75db22097118.png' style="vertical-align:middle;" width="222" height="72" alt="\left( \begin{array}{cc} a & b \\ 2c & 2d \end{array} \right) = \left( \begin{array}{cc} 3 & -1 \\ 1 & 2 \end{array} \right)" title="\left( \begin{array}{cc} a & b \\ 2c & 2d \end{array} \right) = \left( \begin{array}{cc} 3 & -1 \\ 1 & 2 \end{array} \right)"></p> <p>Tenemos una igualdad de matrices, por tanto podemos igualar elemento a elemento y tendríamos:</p> <p><img src='https://matematicasies.com/local/cache-TeX/ee1bace38dbc7056127a0b2ca939f6e4.png' style="vertical-align:middle;" width="50" height="38" alt="a = 3" title="a = 3"> <br><img src='https://matematicasies.com/local/cache-TeX/816c0481b7979c2b22f7975201c0b57e.png' style="vertical-align:middle;" width="63" height="40" alt="b=-1" title="b=-1"> <br><img src='https://matematicasies.com/local/cache-TeX/ef5dfdc5b0b4794b2331372cbe9224e1.png' style="vertical-align:middle;" width="165" height="42" alt="2c=1 \longrightarrow c= 1/2" title="2c=1 \longrightarrow c= 1/2"> <br><img src='https://matematicasies.com/local/cache-TeX/a5e73325cf23469ab36ba589ea44e52e.png' style="vertical-align:middle;" width="148" height="40" alt="2d=2 \longrightarrow d=1" title="2d=2 \longrightarrow d=1"></p> <p>Por lo tanto la matriz es<br class="autobr"> <img src='https://matematicasies.com/local/cache-TeX/aca95c4685029f4fe00b6c5cee27c6a1.png' style="vertical-align:middle;" width="162" height="72" alt="X= \left( \begin{array}{cc} 3 & -1 \\ 1/2 & 1 \end{array} \right)" title="X= \left( \begin{array}{cc} 3 & -1 \\ 1/2 & 1 \end{array} \right)"><br class="autobr"> </p>

2012-06-13T10:28:02Z https://matematicasies.com/Selectividad-Andalucia-2011-5-B1#comment999 2012-06-13T10:28:02Z

<p>esta muy bien explicadoo lo qe no entiendo es la constante C!!!!!!!</p>