document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=985488>Question 985488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations using the methods of matrix row reduction.<BR>\n" );
document.write( "2x+y+2z=0<BR>\n" );
document.write( "4x+3y-z=1<BR>\n" );
document.write( "5x-4y+3z=-41\r<BR>\n" );
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document.write( "What is the solution? \r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606320 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=606320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2B2z=0 ALIGN=MIDDLE  ALT=\"2x%2By%2B2z=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B3y-z=1 ALIGN=MIDDLE  ALT=\"4x%2B3y-z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-4y%2B3z=-41 ALIGN=MIDDLE  ALT=\"5x-4y%2B3z=-41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A2%2C1%2C2%2C0%2C%0D%0A4%2C3%2C-1%2C1%2C%0D%0A5%2C-4%2C3%2C-41%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Step 1: Swap row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A5%2C-4%2C3%2C-41%2C%0D%0A4%2C3%2C-1%2C1%2C%0D%0A2%2C1%2C2%2C0%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Step 2: Divide row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0.6%2C-8.2%2C%0D%0A4%2C3%2C-1%2C1%2C%0D%0A2%2C1%2C2%2C0%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 3: Subtract (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2A+row+%7B%7B%7B1 ALIGN=MIDDLE  ALT=\"4+%2A+row+%7B%7B%7B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		  <BR>\n" );
document.write( " 		<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0.6%2C-8.2%2C%0D%0A0%2C6.2%2C-3.4%2C33.8%2C%0D%0A2%2C1%2C2%2C0%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Step 4: Subtract (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		 <BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0.6%2C-8.2%2C%0D%0A0%2C6.2%2C-3.4%2C33.8%2C%0D%0A0%2C2.6%2C0.8%2C16.4%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > 	<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Step 5: Divide row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.2 ALIGN=MIDDLE  ALT=\"6.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		 <BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0.6%2C-8.2%2C%0D%0A0%2C1%2C-0.548%2C5.452%2C%0D%0A0%2C2.6%2C0.8%2C16.4%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 6:<BR>\n" );
document.write( " Subtract (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.6+ ALIGN=MIDDLE  ALT=\"2.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >* row<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		  <BR>\n" );
document.write( " 		<BR>\n" );
document.write( " 	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0.6%2C-8.2%2C%0D%0A0%2C1%2C-0.548%2C5.452%2C%0D%0A0%2C0%2C2.226%2C2.226%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
document.write( "\n" );
document.write( "Step 7: Divide row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.226 ALIGN=MIDDLE  ALT=\"2.226\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "	 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0.6%2C-8.2%2C%0D%0A0%2C1%2C-0.548%2C5.452%2C%0D%0A0%2C0%2C1%2C1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Matrix is now in row echelon form\r<BR>\n" );
document.write( "\n" );
document.write( "Step 8: Subtract (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6 ALIGN=MIDDLE  ALT=\"0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > * row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0%2C-8.8%2C%0D%0A0%2C1%2C-0.548%2C5.452%2C%0D%0A0%2C0%2C1%2C1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  \r<BR>\n" );
document.write( "\n" );
document.write( "Step 9: Subtract (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.548 ALIGN=MIDDLE  ALT=\"-0.548\"   DISABLED_style= \"max-width:90%; height:auto;\" > * row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		 <BR>\n" );
document.write( "	 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C-0.8%2C0%2C-8.8%2C%0D%0A0%2C1%2C0%2C6%2C%0D%0A0%2C0%2C1%2C1%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Step 10: Subtract (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.8 ALIGN=MIDDLE  ALT=\"-0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > * row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) from row <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " 		 <BR>\n" );
document.write( "	 <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-4%2C%0D%0A0%2C1%2C0%2C6%2C%0D%0A0%2C0%2C1%2C1%29+%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C4%2C%0D%0A1%2C0%2C0%2C-4%2C%0D%0A0%2C1%2C0%2C6%2C%0D%0A0%2C0%2C1%2C1%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >		 \r<BR>\n" );
document.write( "\n" );
document.write( "Matrix is now in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=reduced ALIGN=MIDDLE  ALT=\"reduced\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+row ALIGN=MIDDLE  ALT=\"+row\"   DISABLED_style= \"max-width:90%; height:auto;\" > echelon form.\r<BR>\n" );
document.write( "\n" );
document.write( "solution:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1 ALIGN=MIDDLE  ALT=\"z=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "check:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2B2z=0 ALIGN=MIDDLE  ALT=\"2x%2By%2B2z=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-4%29%2B6%2B2%2A1=0 ALIGN=MIDDLE  ALT=\"2%28-4%29%2B6%2B2%2A1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2B8=0 ALIGN=MIDDLE  ALT=\"-8%2B8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );