2.1

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=24 BGCOLOR="#006666" TEXT="#080000"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Bell MT" ><B>Álgebra lineal</B></FONT><FONT SIZE="4" COLOR="#FFFFCC" FACE="Bell MT" ><B> </B></FONT><FONT SIZE="2" COLOR="#FFFFCC" FACE="Bell MT" ><B>   </B></FONT><B> |     </B><A HREF="index.htm" TARGET="_top" TITLE="Á l g e b r a l i n e a l"><U><B>Página principa</B></U></A><B>l  |  </B><A HREF="id17.htm" TARGET="_top" TITLE="Contenido"><U><B>Contenido</B></U></A><B>  |  </B><A HREF="id26.htm" TARGET="_top" TITLE="Stanley Grossman"><U><B>Grossman</B></U></A></div> <div> </div> </td> </tr><tr> <td valign="top" width=160 BGCOLOR="#FFFFFF" TEXT="#080000"> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-6266400581769473" data-ad-slot="5543838917"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> </td> <td valign="top" height=456 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>Vectores y matrices</B></div> <div> <B>Problemas 2.1</B></div> <div>  <A NAME="arriba"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>arriba</div> <div> <TABLE BORDER="0" CELLPADDING="4" CELLSPACING="1" WIDTH="904" BORDERCOLORLIGHT="#006666" BORDERCOLORDARK="#006666" FRAME="VOID" RULES="NONE" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=3 BGCOLOR=#006666 HEIGHT= 23 WIDTH="878"><div> <B>Definiciones generales</B></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 45 WIDTH="292"><div> <A HREF="#vector_renglón_de_n_componentes" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Vector renglón de </U></A><A HREF="#vector_renglón_de_n_componentes" TITLE="2.1"><U><I>n</I></U></A><A HREF="#vector_renglón_de_n_componentes" TITLE="2.1"><U> componentes</U></A></div> </tD> <tD VALIGN=TOP WIDTH="292"><div> <A HREF="#vector_renglón_de_n_componentes_1" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Vector columna de </U></A><A HREF="#vector_renglón_de_n_componentes_1" TITLE="2.1"><U><I>n</I></U></A><A HREF="#vector_renglón_de_n_componentes_1" TITLE="2.1"><U> componentes</U></A></div> </tD> <tD VALIGN=TOP WIDTH="292"><div> <A HREF="#conjunto_de_todos_los_vectores_de" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Conjunto de todos los vectores de dimensión </U></A><A HREF="#conjunto_de_todos_los_vectores_de" TITLE="2.1"><U><I>n</I></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 23 WIDTH="292"><div> <A HREF="#definición_de_matriz" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Definición de Matriz</U></A></div> </tD> <tD VALIGN=TOP WIDTH="292"><div> <A HREF="#igualdad_de_matrices" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Igualdad de matrices</U></A></div> </tD> <tD VALIGN=TOP WIDTH="292"><div> <A HREF="#suma_de_matrices" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Suma de matrices</U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 45 WIDTH="292"><div> <A HREF="#multiplicación_de_una_matriz_por_un" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Multiplicación de una matriz por un escalar</U></A></div> </tD> <tD VALIGN=TOP COLSPAN=2 WIDTH="585"><div> <A HREF="#teorema_2_1_1" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Teorema 2.1.1</U></A> (Propiedades básicas sobre la suma de matrices y la multiplicación por escalares)</div> </tD> </tR> <tR> <tD VALIGN=TOP BGCOLOR=#CCFFFF HEIGHT= 23 ><NOBR><div> <A HREF="#enunciados_de_los_problemas_2_1" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Enunciados de los ejercicios</U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="292"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="23" ALIGN="bottom" WIDTH="292" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP BGCOLOR=#CCFFCC><NOBR><div> <A HREF="#soluciones_de_los_problemas_2_1" TITLE="2.1"><U><IMG BORDER="0" SRC="Symb075c00b7011866660000.gif" HEIGHT="19" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Soluciones de los ejercicios</U></A></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 BGCOLOR=#006666 HEIGHT= 23 WIDTH="878"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="23" ALIGN="bottom" WIDTH="878" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <div>  <A NAME="vector_renglón_de_n_componentes"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Vector renglón de <I>n</I> componentes</div> <div> <B>Vector renglón de </B><I><B>n</B></I><B> c</B><B>om</B><B>ponentes</B></div> <div> Un vector renglón de <I>n</I> componentes se define como un conjunto <FONT SIZE="4" COLOR="#009933" FACE="Georgia" >ordenado</FONT> de <I>n</I> números escritos de la siguiente manera:</div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="4d28c1c0.gif" border=0 width="140" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="4d171350.gif" border=0 width="881" height="53" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="vector_renglón_de_n_componentes_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Vector renglón de <I>n</I> componentes</div> <div> <B>Vector columna de </B><I><B>n</B></I><B> compo</B><B>nentes</B></div> <div> Un vector columna de <I>n</I> componentes se define como un conjunto <FONT SIZE="4" COLOR="#009933" FACE="Georgia" >ordenado</FONT> de <I>n</I> números escritos de la siguiente manera:</div> <DIV ALIGN="LEFT"></DIV> <div> <B><IMG SRC="4d328690.gif" border=0 width="40" height="105" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <IMG SRC="4d633490.gif" border=0 width="819" height="73" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="conjunto_de_todos_los_vectores_de"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Conjunto de todos los vectores de dimensión <I>n</I></div> <div> <B>Conjunto de todos los vectores de dimensión </B><I><B>n</B></I></div> <div> <IMG SRC="4d5d8a90.gif" border=0 width="728" height="169" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="4d7d8a90.gif" border=0 width="728" height="169" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="definición_de_matriz"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Definición de Matriz</div> <div> <B>Definición de Matriz</B></div> <div> <B><IMG SRC="4d8fc2c0.gif" border=0 width="764" height="44" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <DIV ALIGN="LEFT"></DIV> <div> <B><IMG SRC="4d937ac0.gif" border=0 width="311" height="172" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B><IMG SRC="4dad9a70.gif" border=0 width="729" height="167" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" >triz cuadrada</FONT></div> <div> <B>Matriz cuadrada</B></div> <div> <B><IMG SRC="4df91170.gif" border=0 width="657" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div> <B>Matriz cero</B></div> <div> Una matriz <I>m </I>x <I>n </I>con todos los elementos iguales a 0 se denomina <FONT SIZE="4" COLOR="#009933" FACE="Georgia" >matriz cero</FONT> de <I>m </I>x <I>n.</I></div> <div> <B>Tamaño de una matriz</B></div> <div> Se dice que una matriz <I>m </I>x <I>n </I>tiene tamaño <I>m </I>x <I>n.</I></div> <bR> <div>  <A NAME="igualdad_de_matrices"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Igualdad de matrices</div> <div> <B>Igualdad de matrices</B></div> <div> <B><IMG SRC="4e0b75b0.gif" border=0 width="439" height="91" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="suma_de_matrices"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Suma de matrices</div> <div> <B>Suma de matrices</B></div> <div> <B><IMG SRC="4e198990.gif" border=0 width="920" height="153" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="multiplicación_de_una_matriz_por_un"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Multiplicación de una matriz por un escalar</div> <div> <B>Multiplicaci</B><B>ón</B><B> de una matriz por un escalar</B></div> <div> <B><IMG SRC="4e298990.gif" border=0 width="920" height="153" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="teorema_2_1_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Teorema 2.1.1</div> <div> <B>Teorema 2.1.1</B></div> <div> <B><IMG SRC="4e3f0ec0.gif" border=0 width="752" height="236" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></div> <div>  <A NAME="enunciados_de_los_problemas_2_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>Enunciados de los problemas 2.1</div> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados de los problemas 2.1</B></div> <bR> <div> <B>E</B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" >n los problemas </FONT>1<FONT SIZE="4" COLOR="#000000" FACE="Georgia" > a </FONT>14<FONT SIZE="4" COLOR="#000000" FACE="Georgia" >, realice los cálculos indicados con:</FONT></div> <div> <IMG SRC="1d6ec4f0.gif" border=0 width="236" height="79" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >1.</FONT>  <B>a</B> +<B> b </B><FONT SIZE="4" COLOR="#003333" FACE="Georgia" ><A HREF="#1" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </FONT><FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >6.</FONT>  2<B>a</B> <FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT><B> </B>5<B>b </B><FONT SIZE="4" COLOR="#003333" FACE="Georgia" ><A HREF="#6" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </FONT><FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >13.</FONT>  3<B>b</B> <FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT><B> </B>7<B>c + </B>2<B>a </B><FONT SIZE="4" COLOR="#003333" FACE="Georgia" ><A HREF="#13" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <bR> <div> <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >E</FONT>n los problemas <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >15</FONT> a <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >26</FONT> realice los cálculos indicados con <B>a </B>= (2  <FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT>3  0), <B>b </B>= (<FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT>7  <FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT>5  4) y <B>c = </B> (6  1  8).</div> <div> <FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >15. </FONT><B>b</B> +<B> </B><B>c </B><FONT SIZE="4" COLOR="#003333" FACE="Georgia" ><A HREF="#15" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </FONT><FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >18. </FONT><FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT>2<B>b </B><FONT SIZE="4" COLOR="#111111" FACE="Georgia" ><A HREF="#18" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </FONT><FONT SIZE="4" COLOR="#CC0033" FACE="Georgia" >24. </FONT>3<B>a </B><FONT SIZE="4" COLOR="#000000" FACE="Symbol" >- </FONT>2<B>b</B> <FONT SIZE="4" COLOR="#000000" FACE="Symbol" >-</FONT><B> </B>4<B>c</B><B> </B><FONT SIZE="4" COLOR="#111111" FACE="Georgia" ><A HREF="#24" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <bR> <div> <B>E</B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" >n los problemas </FONT>27<FONT SIZE="4" COLOR="#000000" FACE="Georgia" > a </FONT>43<FONT SIZE="4" COLOR="#000000" FACE="Georgia" >, realice las operaciones indicadas con:</FONT></div> <div> <IMG SRC="52c70470.gif" border=0 width="368" height="71" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><I><IMG SRC="53639140.gif" border=0 width="57" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </I></FONT><A HREF="#27" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="52f61140.gif" border=0 width="97" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#31" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="53189140.gif" border=0 width="137" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#34" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="53388140.gif" border=0 width="136" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#38" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="53568180.gif" border=0 width="616" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#40" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="5377b180.gif" border=0 width="891" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#42" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="53a88310.gif" border=0 width="904" height="49" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#44" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <B>E</B><FONT SIZE="4" COLOR="#000000" FACE="Georgia" >n los problemas </FONT>46<FONT SIZE="4" COLOR="#000000" FACE="Georgia" > a </FONT>57<FONT SIZE="4" COLOR="#000000" FACE="Georgia" >, realice las operaciones indicadas con:</FONT></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="53ce3470.gif" border=0 width="483" height="71" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <FONT SIZE="4" COLOR="#000000" FACE="Georgia" ><IMG SRC="53d80140.gif" border=0 width="128" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> </FONT><A HREF="#50" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="53f88140.gif" border=0 width="136" height="20" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#53" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><IMG SRC="5419c180.gif" border=0 width="668" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#55" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="54398180.gif" border=0 width="920" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#57" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="545b5240.gif" border=0 width="949" height="36" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#59" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="54840370.gif" border=0 width="832" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#60" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="54965480.gif" border=0 width="869" height="72" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="54ca1840.gif" border=0 width="161" height="132" ALT="Imagen de Paintbrush" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#63" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="551dd7d0.gif" border=0 width="733" height="125" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><A HREF="#65" TITLE="2.1"><U><IMG SRC="12718180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <DIV ALIGN="LEFT"></DIV> <div>  <A NAME="soluciones_de_los_problemas_2_1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>oluciones de los problemas 2.1</div> <div> <B>Soluciones de los problemas 2.1</B></div> <div> | <A HREF="#1" TITLE="2.1"><U>1</U></A> | <A HREF="#6" TITLE="2.1"><U>6</U></A> | <A HREF="#13" TITLE="2.1"><U>13</U></A> | <A HREF="#15" TITLE="2.1"><U>15</U></A> | <A HREF="#18" TITLE="2.1"><U>18</U></A> | <A HREF="#24" TITLE="2.1"><U>24</U></A> | <A HREF="#27" TITLE="2.1"><U>27</U></A> | <A HREF="#31" TITLE="2.1"><U>31</U></A> | <A HREF="#34" TITLE="2.1"><U>34</U></A> | <A HREF="#38" TITLE="2.1"><U>38</U></A> | <A HREF="#40" TITLE="2.1"><U>40</U></A> | <A HREF="#42" TITLE="2.1"><U>42</U></A> | <A HREF="#44" TITLE="2.1"><U>44</U></A> | <A HREF="#50" TITLE="2.1"><U>50</U></A> | <A HREF="#53" TITLE="2.1"><U>53</U></A> | <A HREF="#55" TITLE="2.1"><U>55</U></A> | <A HREF="#57" TITLE="2.1"><U>57</U></A> | <A HREF="#59" TITLE="2.1"><U>59</U></A> | <A HREF="#60" TITLE="2.1"><U>60</U></A> | <A HREF="#63" TITLE="2.1"><U>63</U></A> | <A HREF="#65" TITLE="2.1"><U>65</U></A> |</div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="1d9ac810.gif" border=0 width="428" height="129" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="1db31850.gif" border=0 width="817" height="133" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <IMG SRC="1dd54810.gif" border=0 width="852" height="129" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>15</div> <div> <IMG SRC="529c5740.gif" border=0 width="709" height="116" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>18</div> <div> <IMG SRC="52a9f770.gif" border=0 width="671" height="119" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="24"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>24</div> <div> <IMG SRC="52b74930.gif" border=0 width="884" height="147" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="27"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>27</div> <div> <IMG SRC="52d24870.gif" border=0 width="548" height="135" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="31"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>31</div> <div> <IMG SRC="52e44190.gif" border=0 width="836" height="281" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="34"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>34</div> <div> <IMG SRC="5307f6c0.gif" border=0 width="895" height="364" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="38"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>38</div> <div> <IMG SRC="532180f0.gif" border=0 width="792" height="271" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="40"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>40</div> <div> <IMG SRC="53477c70.gif" border=0 width="887" height="199" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="42"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>42</div> <div> <IMG SRC="538cc590.gif" border=0 width="972" height="345" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="44"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>44</div> <div> <IMG SRC="53b88070.gif" border=0 width="904" height="263" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="50"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>50</div> <div> <IMG SRC="53eb76c0.gif" border=0 width="951" height="364" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="53"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>53</div> <div> <IMG SRC="5408d570.gif" border=0 width="909" height="343" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="55"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>55</div> <div> <IMG SRC="54271570.gif" border=0 width="881" height="343" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="57"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>57</div> <div> <IMG SRC="54498a10.gif" border=0 width="920" height="417" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="59"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>59</div> <div> <IMG SRC="546c8d70.gif" border=0 width="968" height="471" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="60"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>60</div> <div> <IMG SRC="54740410.gif" border=0 width="832" height="833" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="63"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>63</div> <div> <IMG SRC="54e65480.gif" border=0 width="869" height="72" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="54da1840.gif" border=0 width="161" height="132" ALT="Imagen de Paintbrush" ALIGN="LEFT" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="54fc4330.gif" border=0 width="452" height="307" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="65"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>65</div> <div> <IMG SRC="550bdab0.gif" border=0 width="957" height="427" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-6266400581769473" data-ad-slot="7846235711"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <B>Lista de los Problemas del álgebra lineal (Ed. 7) de Stanley Grossman</B></div> <div> <B>|</B> <A HREF="id28.htm" TARGET="_top" TITLE="Problemas 1.1"><U>Problemas 1.1</U></A> | <A HREF="id29.htm" TARGET="_top" TITLE="1.2"><U>Problemas 1.2</U></A> | <A HREF="id30.htm" TARGET="_top" TITLE="1.4"><U>Problemas 1.4</U></A> | <A HREF="id32.htm" TARGET="_top" TITLE="2.1"><U>Problemas 2.1</U></A> | <A HREF="id112.htm" TARGET="_top" TITLE="5.1"><U>Problemas 5.1</U></A> |</div> <bR> <bR> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="0f028280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="0f128280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="http://www.youtube.com/user/MatematicaAp"><U><IMG SRC="0f228280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> <a href="HTMLobj-1205/Aviso_Baldor.docx"><img align="bottom" border="0" width="40" height="40" src="HTMLobj-1205/gato_1.jpg"></a>  </div> <div>  <a href="http://twitter.com/Calculo21" class="twitter-follow-button" data-button="grey" data-text-color="#FFFFFF" data-link-color="#00AEFF" data-show-count="false" data-lang="es">Follow @Calculo21</a> <script src="http://platform.twitter.com/widgets.js" type="text/javascript"></script>  </div> <bR> <div> <B>|  </B><A HREF="index.htm" TARGET="_top" TITLE="Á l g e b r a l i n e a l"><U><B>Página principal</B></U></A><B>  |  </B><A HREF="id17.htm" TARGET="_top" TITLE="Contenido"><U><B>Contenido</B></U></A><B>   |   </B><A HREF="id18.htm" TARGET="_top" TITLE="email"><U><B>e-mail</B></U></A><B>   |   </B><A HREF="id19.htm" TARGET="_top" TITLE="Enlaces"><U><B>Enlaces</B></U></A><B>  |</B></div> <bR> </td> </tr></table></body>