document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=877521>Question 877521</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This homework problem has been stumping me. <BR>\n" );
document.write( "I am given this matrix: <BR>\n" );
document.write( "Matrix M = {{1,0,2},{-1,1,2},{-1,-1,2}} <BR>\n" );
document.write( "Then asked to solve this equation: <BR>\n" );
document.write( "M^3 + xM^2 + yM + zI = 0 <BR>\n" );
document.write( "I is the 3x3 identity matrix. x, y, and z are constants<BR>\n" );
document.write( "Any hints on how to get started would be appreciated! Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530094 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=530094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=%28matrix%283%2C3%2C1%2C0%2C2%2C-1%2C1%2C2%2C-1%2C-1%2C2%29%29 ALIGN=MIDDLE  ALT=\"M=%28matrix%283%2C3%2C1%2C0%2C2%2C-1%2C1%2C2%2C-1%2C-1%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=yM=+%28matrix%283%2C3%2Cy%2C0%2C2y%2C-y%2Cy%2C2y%2C-y%2C-y%2C2y%29%29+ ALIGN=MIDDLE  ALT=\"yM=+%28matrix%283%2C3%2Cy%2C0%2C2y%2C-y%2Cy%2C2y%2C-y%2C-y%2C2y%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5E2=%28matrix%283%2C3%2C-1%2C-2%2C6%2C-4%2C-1%2C4%2C-2%2C-3%2C0%29%29 ALIGN=MIDDLE  ALT=\"M%5E2=%28matrix%283%2C3%2C-1%2C-2%2C6%2C-4%2C-1%2C4%2C-2%2C-3%2C0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xM%5E2=+%28matrix%283%2C3%2C-x%2C-2x%2C6x%2C-4x%2C-x%2C4x%2C-2x%2C-3x%2C0%29%29+ ALIGN=MIDDLE  ALT=\"xM%5E2=+%28matrix%283%2C3%2C-x%2C-2x%2C6x%2C-4x%2C-x%2C4x%2C-2x%2C-3x%2C0%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5E3=%28matrix%283%2C3%2C-5%2C-8%2C6%2C-7%2C-5%2C-2%2C1%2C-3%2C-10%29%29 ALIGN=MIDDLE  ALT=\"M%5E3=%28matrix%283%2C3%2C-5%2C-8%2C6%2C-7%2C-5%2C-2%2C1%2C-3%2C-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I=%28matrix%283%2C3%2C1%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C1%29%29 ALIGN=MIDDLE  ALT=\"I=%28matrix%283%2C3%2C1%2C0%2C0%2C0%2C1%2C0%2C0%2C0%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zI=+%28matrix%283%2C3%2Cz%2C0%2C0%2C0%2Cz%2C0%2C0%2C0%2Cz%29%29+ ALIGN=MIDDLE  ALT=\"zI=+%28matrix%283%2C3%2Cz%2C0%2C0%2C0%2Cz%2C0%2C0%2C0%2Cz%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5E3%2BxM%5E2%2ByM%2BzI=0 ALIGN=MIDDLE  ALT=\"M%5E3%2BxM%5E2%2ByM%2BzI=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-5%2C-8%2C6%2C-7%2C-5%2C-2%2C1%2C-3%2C-10%29%29%2B%28matrix%283%2C3%2C-x%2C-2x%2C6x%2C-4x%2C-x%2C4x%2C-2x%2C-3x%2C0%29%29%2B%28matrix%283%2C3%2Cy%2C0%2C2y%2C-y%2Cy%2C2y%2C-y%2C-y%2C2y%29%29%2B%28matrix%283%2C3%2Cz%2C0%2C0%2C0%2Cz%2C0%2C0%2C0%2Cz%29%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-x%2C-2x%2C6x%2C-4x%2C-x%2C4x%2C-2x%2C-3x%2C0%29%29%2B%28matrix%283%2C3%2Cy%2C0%2C2y%2C-y%2Cy%2C2y%2C-y%2C-y%2C2y%29%29%2B%28matrix%283%2C3%2Cz%2C0%2C0%2C0%2Cz%2C0%2C0%2C0%2Cz%29%29=%28matrix%283%2C3%2C5%2C8%2C-6%2C7%2C5%2C2%2C-1%2C3%2C10%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ".<BR>\n" );
document.write( "Using the first row of matrix elements,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2By%2Bz=5 ALIGN=MIDDLE  ALT=\"-x%2By%2Bz=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x=8 ALIGN=MIDDLE  ALT=\"-2x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B2y=-6 ALIGN=MIDDLE  ALT=\"6x%2B2y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Which leads to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-8 ALIGN=MIDDLE  ALT=\"z=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "All three rows yield the same results so it is consistent.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );