document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257807>Question 257807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the row echelon method to solve the system of three equations in three unknowns.<BR>\n" );
document.write( "x - y + 2z =  -2<BR>\n" );
document.write( "5x + z = 0<BR>\n" );
document.write( "x + 2y+z =   4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189697 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given the following:<BR>\n" );
document.write( "x - y + 2z = -2<BR>\n" );
document.write( "5x + z = 0<BR>\n" );
document.write( "x + 2y+z = 4<BR>\n" );
document.write( "--<BR>\n" );
document.write( "in row echelon form, we have:<BR>\n" );
document.write( "1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2)<BR>\n" );
document.write( "5 . . . . . .0 . . . . . . . .1 . . . . . . .0<BR>\n" );
document.write( "1 . . . . . . 2 . . . . . . . 1 . . . . . .. 4<BR>\n" );
document.write( "We need to get a diagonal matrix so take row 2 - 5 row 1 -> row 2; row 3 - row 1 -> row 3<BR>\n" );
document.write( "--<BR>\n" );
document.write( "1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2)<BR>\n" );
document.write( "0 . . . .. . 5 . . . . . . . .(-9) . . .. . . 10<BR>\n" );
document.write( "0 . . . .. . 3 . . . . . .. . . -1 . . . . . . . 6<BR>\n" );
document.write( "(1/5) row 2 -> row 2<BR>\n" );
document.write( "--<BR>\n" );
document.write( "1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2)<BR>\n" );
document.write( "0 . . . . . . 1 . . . . . . . .(-9/5) . .  2<BR>\n" );
document.write( "0 . . . . . . 1 . . . . . . . .3 . . . . . . . 6<BR>\n" );
document.write( "row 1 + row 2 -> row 1; row 3 - row 2 -> row 3<BR>\n" );
document.write( "--<BR>\n" );
document.write( "1 . . . . . . 0. . . . . . . .(1/5)  . . . . 0<BR>\n" );
document.write( "0 . . . . . . 1 . . . . . . . .(-9/5) . . . 2<BR>\n" );
document.write( "0 . . . . . . 0 . . . . . . . .(22/5) . . . .0<BR>\n" );
document.write( "(5/24) row 3 -> row 3<BR>\n" );
document.write( "--<BR>\n" );
document.write( "1 . . . . . . 0. . . . . . . .(1/5)  . . . . 0<BR>\n" );
document.write( "0 . . . . . . 1 . . . . . . . .(-9/5) . . . 2<BR>\n" );
document.write( "0 . . . . . . 0 . . . . . . . .1 . . . . . . . 0<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "z = 0<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "{0, 2, 0} </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );