document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164526>Question 1164526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose A is an invertible n × n matrix. Must the system of equations A x = x have a unique solution? Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788932 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "No.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The matrix equation  &nbsp;Ax = x  &nbsp;means that the matrix  &nbsp;A&nbsp;  has an eigenvalue equal to &nbsp;1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Far not every square invertible matrix &nbsp;A &nbsp;has eigenvalue &nbsp;1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A contradictory example is any &nbsp;2x2-matrix of the rotation by angle &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;in the coordinate plane with\r<BR>\n" );
document.write( "\n" );
document.write( "the rotation angle  &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;different from  &nbsp;0 (from zero or from any multiple of the full angle &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solved, answered and explained.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );