document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=293780>Question 293780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the problem if there exist solutions of the homogeneous system of linear equations other than x=0, express the general solution as a linear combination of linearly independent column vectors.\r<BR>\n" );
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document.write( "  x_1  +  2x_2  -     x_3  =  0<BR>\n" );
document.write( "2x_1  +    x_2  +    x_3  =  0<BR>\n" );
document.write( "  x_1   -    x_2  +  2x_3  =  0\r<BR>\n" );
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document.write( "(x_1 means x subscript of 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211990 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> change <BR>\n" );
document.write( "x_1 to x<BR>\n" );
document.write( "x_2 to y<BR>\n" );
document.write( "x_3 to z\r<BR>\n" );
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document.write( "x+2y-z=0, <BR>\n" );
document.write( "2x+y+z=0,<BR>\n" );
document.write( "x-y+2z=0<BR>\n" );
document.write( "x=z-2y<BR>\n" );
document.write( "z-2y=-y+2z<BR>\n" );
document.write( "z=-y<BR>\n" );
document.write( "y=-x<BR>\n" );
document.write( "z=-x<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );