document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177515>Question 1177515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you help me on how to do part b) and if I am correct in the other sections?\r<BR>\n" );
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document.write( "Let V=R2, let H be the subset of V of all points on the line y=−4x, and let K be the subset of V of all points on the line y=−3x. Is H∪K a subspace of the vector space V?<BR>\n" );
document.write( "a)Does H∪K contain the zero vector of V? Answer:H union K contains the zero vector og V\r<BR>\n" );
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document.write( "b)Is H∪K closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H∪K whose sum is not in H∪K, using a comma separated list and syntax such as <1,2>, <3,4>.<BR>\n" );
document.write( "Answer:\r<BR>\n" );
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document.write( "c)Is H∪K closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H∪K whose product is not in H∪K, using a comma separated list and syntax such as 2, <3,4>.<BR>\n" );
document.write( "Answer:Closed\r<BR>\n" );
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document.write( "d)Is H∪K a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your answers to parts 1-3.<BR>\n" );
document.write( "Answer: H union K is not a subspace of V.<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 #811432 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811432\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "There is only one vector in the union of H and K, namely <0,0>\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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