document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888422>Question 888422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use matrices to solve this system:<BR>\n" );
document.write( "2x+3y+z=2<BR>\n" );
document.write( "5x-2y-z=4<BR>\n" );
document.write( "x-y-2z=-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537385 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=537385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x+3y+z=2<BR>\n" );
document.write( "5x-2y-z=4<BR>\n" );
document.write( "x-y-2z=-3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2,3,1,2<BR>\n" );
document.write( "5,-2,-1,4<BR>\n" );
document.write( "1,-1,-2,-3\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 1 by 2/1<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "5,-2,-1,4<BR>\n" );
document.write( "1,-1,-2,-3\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-5/1) *row 1 to row 2<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "0,-19/2,-7/2,-1<BR>\n" );
document.write( "1,-1,-2,-3\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (-1/1) *row 1 to row 3<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "0,-19/2,-7/2,-1<BR>\n" );
document.write( "0,-5/2,-5/2,-4\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 2 by -19/2<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "0,1,-14/-38,-2/-19<BR>\n" );
document.write( "0,-5/2,-5/2,-4\r<BR>\n" );
document.write( "\n" );
document.write( "add  down (5/2) *row 2 to row 3<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "0,1,7/19,2/19<BR>\n" );
document.write( "0,0,-120/76,-142/38\r<BR>\n" );
document.write( "\n" );
document.write( "divide row 3 by -30/19<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "0,1,7/19,2/19<BR>\n" );
document.write( "0,0,1,-1349/-570\r<BR>\n" );
document.write( "\n" );
document.write( "We now have the value for the last variable.<BR>\n" );
document.write( "We will work our way up and get the other solutions.\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-7/19) *row 3 to row 2<BR>\n" );
document.write( "1,3/2,1/2,1<BR>\n" );
document.write( "0,1,0,-8303/10830<BR>\n" );
document.write( "0,0,1,71/30\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-1/2) *row 3 to row 1<BR>\n" );
document.write( "1,6/4,0,-11/60<BR>\n" );
document.write( "0,1,0,-23/30<BR>\n" );
document.write( "0,0,1,71/30\r<BR>\n" );
document.write( "\n" );
document.write( "add up  (-3/2) *row 2 to row 1<BR>\n" );
document.write( "1,0,0,3480/3600<BR>\n" );
document.write( "0,1,0,-23/30<BR>\n" );
document.write( "0,0,1,71/30\r<BR>\n" );
document.write( "\n" );
document.write( "final<BR>\n" );
document.write( "1,0,0,29/30<BR>\n" );
document.write( "0,1,0,-23/30<BR>\n" );
document.write( "0,0,1,71/30\r<BR>\n" );
document.write( "\n" );
document.write( "1,0,0,29/30 = 0.96666667<BR>\n" );
document.write( "0,1,0,-23/30 = -0.76666667<BR>\n" );
document.write( "0,0,1,71/30 = 2.36666667<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );