document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26495>Question 26495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a homework problem that I don't know how to do. <BR>\n" );
document.write( "I'm asked to solve the following problem;\r<BR>\n" );
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document.write( "For what values of h is v3 in span {v1,v2} and for what values of h is {v1,v2,v3}linearly dependent?<BR>\n" );
document.write( "given that    <BR>\n" );
document.write( "              <BR>\n" );
document.write( "----[ 1]-----[-2]------[ 2]<BR>\n" );
document.write( "v1=[-5]-v2=[10]--v3=[-9]<BR>\n" );
document.write( "----[-3]-----[ 6]-------[ h]<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 #14373 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have a homework problem that I don't know how to do. <BR>\n" );
document.write( "I'm asked to solve the following problem; <BR>\n" );
document.write( "For what values of h is v3 in span {v1,v2} and for what values of h is {v1,v2,v3}linearly dependent?<BR>\n" );
document.write( "given that \r<BR>\n" );
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document.write( "----[ 1]-----[-2]------[ 2]<BR>\n" );
document.write( "v1=[-5]-v2=[10]--v3=[-9]<BR>\n" );
document.write( "----[-3]-----[ 6]-------[ h]\r<BR>\n" );
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document.write( "LET US TAKE  3D SPACE WITH,I,J AND K AS UNIT VECTORS...SO<BR>\n" );
document.write( "V1=1I-5J-3K<BR>\n" );
document.write( "V2=-2I+10J+6K<BR>\n" );
document.write( "V3=2I-9J+HK<BR>\n" );
document.write( "WE FIND HERE THAT V2=-2V1...SO THEY ARE NOT INDEPENDENT...PLEASE CHECK THE NUMBERS AND COME BACK.HOWEVER ,I AM GIVING THE METHOD OF SOLUTION BELOW..<BR>\n" );
document.write( "IF V3 IS IN V1 AND V2 SPAN ,THEN WE HAVE <BR>\n" );
document.write( "V3=AV1+BV2=<BR>\n" );
document.write( "2I-9J+HK=AI-5AJ-3AK-2BI+10BJ+6BK= I(A-2B)+J(10B-5A)+K(6B-3A)<BR>\n" );
document.write( "HENCE  SOLVE FOR A AND B FROM EQNS.I AND II AND SUBSTITUTE THOSE VALUES IN EQN.III TO GET H VALUE..HERE YOU WILL NOT GET THE ANSWER.<BR>\n" );
document.write( "A-2B=2.......................I<BR>\n" );
document.write( "10B-5A=-9....................II<BR>\n" );
document.write( "6B-3A=H.......................III<BR>\n" );
document.write( "THE ABOVE CASE IS FOR V1,V2,V3 TO BE DEPENDENT.<BR>\n" );
document.write( "SO CHECK YOUR SECOND QUESTION AGAIN..THEY ARE INDEPENDENT OR DEPENDENT?<BR>\n" );
document.write( "IF V1,V2,V3 ARE TO BE INDEPENDENT ,H SHOULD NOT BE EQUAL TO THE VALUE OBTAINED AS ABOVE. </SPAN>\n" );
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