document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210438>Question 1210438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two matrices P and Q are <BR>\n" );
document.write( "┌x²   3┐ and ┌3  6┐respectively. <BR>\n" );
document.write( "│1   3x│     │2  x│<BR>\n" );
document.write( "Given  that P and Q are commutative under matrix multiplication. Find the positive value of x.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852551 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13250)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=matrix%282%2C2%2Cx%5E2%2C3%2C1%2C3x%29 ALIGN=MIDDLE  ALT=\"P=matrix%282%2C2%2Cx%5E2%2C3%2C1%2C3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q=matrix%282%2C2%2C3%2C6%2C2%2Cx%29 ALIGN=MIDDLE  ALT=\"Q=matrix%282%2C2%2C3%2C6%2C2%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The entry in row 2 column 1 of matrix PQ is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%283%29%2B%283x%29%282%29=3%2B6x ALIGN=MIDDLE  ALT=\"%281%29%283%29%2B%283x%29%282%29=3%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The entry in row 2 column 1 of matrix QP is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%28x%5E2%29%2B%28x%29%281%29=2x%5E2%2Bx ALIGN=MIDDLE  ALT=\"%282%29%28x%5E2%29%2B%28x%29%281%29=2x%5E2%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "those entries are the same, so<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B6x=2x%5E2%2Bx ALIGN=MIDDLE  ALT=\"3%2B6x=2x%5E2%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-5x-3=0 ALIGN=MIDDLE  ALT=\"2x%5E2-5x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B1%29%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The positive solution is<br><BR>\n" );
document.write( "ANSWER: x=3<br><BR>\n" );
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