document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465677>Question 465677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> let v1=(-3,2,4), v2=(-3,5,0), and y=(-18,24,h)\r<BR>\n" );
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document.write( "for what value of h is y in the plane spanned by v1 and v2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319316 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C+-3%2C-3%2C-18%2C2%2C5%2C24%2C4%2C0%2Ch%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C+-3%2C-3%2C-18%2C2%2C5%2C24%2C4%2C0%2Ch%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > must have rank less than 3. \r<BR>\n" );
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document.write( "After reducing to row echelon form, the matrix becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C+1%2C1%2C6%2C0%2C1%2C4%2C0%2C0%2C%288-h%29%2F4%29%29%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C+1%2C1%2C6%2C0%2C1%2C4%2C0%2C0%2C%288-h%29%2F4%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "==> h = 8 for linear dependence.\r<BR>\n" );
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document.write( "==> y is in the plane spanned by v1 and v2 if h = 8. </SPAN>\n" );
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