document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165494>Question 165494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the problem:\r<BR>\n" );
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document.write( "Prove that (1,0,0,1) and (0,1,1,0) are linearly independent.  I think they are dependent, am i missing something? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121980 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The previous discussion regarding dot product was not correct. <BR>\n" );
document.write( "I mixed up orthogonality and linear independence. <BR>\n" );
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document.write( "For these two vectors to be linearly independent, then a combination of these two vectors with two scalar multipliers can only be zero when the multipliers are zero.<BR>\n" );
document.write( "(1,0,0,1)A+(0,1,1,0)B=(0,0,0,0) only if A=B=0.<BR>\n" );
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document.write( "Look at each individual component of the vectors.<BR>\n" );
document.write( "1.(1)A+(0)B=0<BR>\n" );
document.write( "2.(0)A+(1)B=0<BR>\n" );
document.write( "3.(0)A+(1)B=0<BR>\n" );
document.write( "4.(1)A+(0)B=0<BR>\n" );
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document.write( "From 1 and 4,<BR>\n" );
document.write( "A=0<BR>\n" );
document.write( "From 2 and 3,<BR>\n" );
document.write( "B=0<BR>\n" );
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document.write( "Therefore, you proved that they are linearly independent because the combination of the two vectors can only equal the zero vector when A=B=0.<BR>\n" );
document.write( "Sorry for the confusion.\r<BR>\n" );
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