document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3683>Question 3683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let u, v, and w be distinct vectors of a vector space V. Show that if <BR>\n" );
document.write( "{u, v, w} is a basis for V, then {u + v + w, v + w, w} is also a basis<BR>\n" );
document.write( "for V.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1633 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=1633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  if a(u + v + w)+ b(v + w) + c w = 0 for scalars a,b,c<BR>\n" );
document.write( " then a u + (a+b)v + (a+b+c)w = 0<BR>\n" );
document.write( " since u,v,w are independent <BR>\n" );
document.write( " we have a = 0, a+b = 0 and a+b+c = 0\r<BR>\n" );
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document.write( " This implies b = 0 and so c = 0.<BR>\n" );
document.write( " This shows u + v + w, v + w, w are three independent<BR>\n" );
document.write( " and so {u + v + w, v + w, w} forms a basis for V,<BR>\n" );
document.write( " because {u,v,w} is a basis of V, dim V = 3.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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