document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4399>Question 4399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a given set, of all polynomials of the form p(t) = a + t^2, where<BR>\n" );
document.write( "a is in R (reals).  How do you determine whether that given set is a subspace<BR>\n" );
document.write( "of P(sub n) for an appropriate value of n? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2012 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=2012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  For a given vector space V, a subset W is a subspace of V if and only<BR>\n" );
document.write( " if av+bw is in W for all v, w in W and scalars a,b.(reals here)<BR>\n" );
document.write( "  <BR>\n" );
document.write( " Now W = {a + t^2| a is real} = set of polynomials in R with<BR>\n" );
document.write( " deg <=2 and the coefficient of t^2 = 1,  the coefficient of t = 0.<BR>\n" );
document.write( " Clearly, W is a subset of P2 = {a + bt + ct^2| a,b,c are reals} <BR>\n" );
document.write( " = set of polynomials in R of degree <=2.\r<BR>\n" );
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document.write( " But, W is not a subspace of P2.<BR>\n" );
document.write( " Since t^2 is in W but t^2 + t^2 = 2t^2 is not in W.  \r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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