document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29494>Question 29494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let a be a fixed vector in R^3, and define W to be the subset of R^3 given by<BR>\n" );
document.write( "W={x: a^Tx=0}. Provce that W is a subspace of R^3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16656 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Don't use a to represent a vector. I use u instead.\r<BR>\n" );
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document.write( " And u^T x means the inner (dot) product of <u, x>\r<BR>\n" );
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document.write( " W={x: u^Tx=0}. Provce that W is a subspace of R^3.\r<BR>\n" );
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document.write( " proof: If x, y in W, a, b in R, then<BR>\n" );
document.write( " u^T (ax+by) = a u^x + b u^y = 0 <BR>\n" );
document.write( " --> W is a subspace.\r<BR>\n" );
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document.write( " (<u, ax+by> = a<u,x> + b<u,y> & <BR>\n" );
document.write( "  <ax+by, u> = a<x,u> + b<y,u> called bilinear)\r<BR>\n" );
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document.write( " You have to work hard.\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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document.write( " </SPAN>\n" );
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