document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=225501>Question 225501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of the matrix: <BR>\n" );
document.write( "1 1 1<BR>\n" );
document.write( "3 5 4<BR>\n" );
document.write( "3 6 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168244 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=168244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(1\ 1\ \,1\cr3\ 5\ 4\cr3\ 6\ 5\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Augment your matrix with the 3X3 identity matrix:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(1\ 1\ \,1\ 1\ 0\ 0\cr3\ 5\ 4\ 0\ 1\ 0\cr3\ 6\ 5\ 0\ 0\ 1\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next use Gauss-Jordan elimination to transform the left-hand 3X3 side of your augmented matrix into the identity matrix, thus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(1\ 0\ 0\ b_{11}\ b_{12}\ b_{13}\cr0\ 1\ 0\ b_{21}\ b_{22}\ b_{23}\cr0\ 0\ 1\ b_{31}\ b_{32}\ b_{33}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The resulting 3X3 on the right, consisting of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b_{11}\"> through <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b_{33}\"> will be your identity matrix.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Fortunately, there is a much easier way.  Go to http://www.bluebit.gr/matrix-calculator/, enter your matrix just like you did here separating the elements with spaces and the rows with carriage returns, check off Matrix Inverse, and then click Calculate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );