document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867004>Question 867004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a Linear Algebra question. <BR>\n" );
document.write( "If Q is the vector space where f(x)=f^2(x) and f(x)=1 is Q a real vector space?<BR>\n" );
document.write( "Assuming it is a subspace of F(Negative Infinity to Infinity) we only need to check the 2 axioms addition and scalar multiplication<BR>\n" );
document.write( "1. Addition f(x) + f(x) = 1 + 1 = 2 <BR>\n" );
document.write( "Here is my question: f(x) = 2 isn't within the space, does that mean we don't have a Real vector space? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522641 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=522641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct. \r<BR>\n" );
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document.write( "According to this <a  rel=nofollow HREF=\"http://www.math.niu.edu/~beachy/courses/240/06spring/vectorspace.html\">link</a>, it says \r<BR>\n" );
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document.write( "<blockquote>     <font color=\"blue\">\"Closure: If u and v are any vectors in V, then the sum   u + v   belongs to V.\"</font><BR>\n" );
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document.write( "Both f(x) = 1 and g(x) = 1 belong to the vector space Q, but h(x) = f(x) + g(x) = 2 does NOT belong to the vector space Q (since h^2(x) = 4, h(x) = 2, h^2(x) doesn't equal h(x))\r<BR>\n" );
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document.write( "So because the closure rule doesn't hold for all elements in Q, this means Q is NOT a vector space. </SPAN>\n" );
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