# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/det(A)=-16<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$det(A)=-16&lt;0$">|; 

$key = q/det(A_0)=1-1=lm=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$det(A_0)=1-1=lm=0$">|; 

$key = q/r(A)=r(A_0)=2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$r(A)=r(A_0)=2$">|; 

$key = q/det(A_0)=lm=4>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$det(A_0)=lm=4&gt;0$">|; 

$key = q/{displaymath}mathrmA=left(array{{rrr}1&-1&-3-1&1&-1-3&-1&1array{right)qquadmathrmA_0=left(array{{rr}1&-1-1&1array{right).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="73" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="\begin{displaymath}
\mathrm A=\left(
\begin{array}{rrr}
1 &amp; -1 &amp; -3\\\\
-1 ...
...
\begin{array}{rr}
1 &amp; -1\\\\
-1 &amp; 1
\end{array}
\right).
\end{displaymath}">|; 

$key = q/det(A_0)=2-displaystylefrac{9}{4}<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$det(A_0)=2-\displaystyle\frac{9}{4}&lt;0$">|; 

$key = q/lx^2-my^2=-c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$lx^2-my^2=-c$">|; 

$key = q/det(A_0)=(16-16^2)<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$det(A_0)=(16-16^2)&lt;0$">|; 

$key = q/x^2+8y^2-4xy-2=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$x^2+8y^2-4xy-2=0$">|; 

$key = q/my^2-lx^2=c;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$my^2-lx^2=c$">|; 

$key = q/x^2-2xy+y^2-6x-2y+1=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$x^2-2xy+y^2-6x-2y+1=0$">|; 

$key = q/p_{A_0}(lambda)=(1-lambda)^2-1=lambda(lambda-2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$p_{A_0}(\lambda)=(1-\lambda)^2-1=\lambda(\lambda-2)$">|; 

$key = q/lx^2-my^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$lx^2-my^2$">|; 

$key = q/x^2+3xy+2y^2-x-y=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$x^2+3xy+2y^2-x-y=0$">|; 

$key = q/{displaymath}mathrmA=left(array{{rrr}1&-2&0-2&8&00&0&-2array{right)qquadmathrmA_0=left(array{{rr}1&-2-2&8array{right).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="73" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="\begin{displaymath}
\mathrm A=\left(
\begin{array}{rrr}
1 &amp; -2 &amp; 0\\\\
-2 &amp;...
...
\begin{array}{rr}
1 &amp; -2\\\\
-2 &amp; 8
\end{array}
\right).
\end{displaymath}">|; 

$key = q/A_0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$A_0$">|; 

$key = q/c=displaystyle-frac{detA}{lm}=frac{5}{2}>0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$c=\displaystyle-\frac{detA}{lm}=\frac{5}{2}&gt;0$">|; 

$key = q/det(A)=displaystylefrac{3}{4}-displaystylefrac{3}{4}=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$det(A)=\displaystyle\frac{3}{4}-\displaystyle\frac{3}{4}=0$">|; 

$key = q/c=displaystyle-frac{detA}{lm}=frac{129}{16-16^2}<0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$c=\displaystyle-\frac{detA}{lm}=\frac{129}{16-16^2}&lt;0$">|; 

$key = q/{displaymath}mathrmA=left(array{{rrr}4&16&-816&4&-displaystylefrac{1}{2}-8&-dispadmathrmA_0=left(array{{cc}4&1616&4array{right).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="367" HEIGHT="98" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="\begin{displaymath}
\mathrm A=\left(
\begin{array}{rrr}
4 &amp; 16 &amp; -8\\\\
16 ...
...
\begin{array}{cc}
4 &amp; 16\\\\
16 &amp; 4
\end{array}
\right).
\end{displaymath}">|; 

$key = q/det(A)=-128-1neq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$det(A)=-128-1\neq 0$">|; 

$key = q/{displaymath}mathrmA=left(array{{rrr}1&displaystylefrac{3}{2}&-displaystylefrac{efrac{3}{2}displaystylefrac{3}{2}&2array{right).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="131" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="\begin{displaymath}
\mathrm A=\left(
\begin{array}{rrr}
1 &amp; \displaystyle\fr...
...3}{2}\\\\
\displaystyle\frac{3}{2} &amp; 2
\end{array}
\right).
\end{displaymath}">|; 

$key = q/4x^2+32xy+4y^2-16x-y=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$4x^2+32xy+4y^2-16x-y=0$">|; 

$key = q/det(A)=-2det(A_0)neq0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$det(A)=-2det(A_0)\neq 0$">|; 

1;

