document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=647443>Question 647443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if you were to use gauss-jordan elimination on the following linear system, what would the augmented matrix be?\r<BR>\n" );
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document.write( "3w-x=2y+z-4<BR>\n" );
document.write( "9x-y+z=10<BR>\n" );
document.write( "4w+3y-z=7<BR>\n" );
document.write( "12x+17=2y-z+6\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406202 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=406202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first write it form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aw+%2B+bx+%2B+cy+%2B+dz+=+k ALIGN=MIDDLE  ALT=\"aw+%2B+bx+%2B+cy+%2B+dz+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for constants \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w+-+x+-+2y+-+z+=+-4 ALIGN=MIDDLE  ALT=\"3w+-+x+-+2y+-+z+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0w+%2B+9x+-+y+%2B+z+=+10 ALIGN=MIDDLE  ALT=\"0w+%2B+9x+-+y+%2B+z+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w+%2B+0x+%2B+3y+-+z+=+7 ALIGN=MIDDLE  ALT=\"4w+%2B+0x+%2B+3y+-+z+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0w+%2B+12x+-+2y+%2B+z+=+-11 ALIGN=MIDDLE  ALT=\"0w+%2B+12x+-+2y+%2B+z+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|3|	-1|	-2|	-1|	-4|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "|4|	0|	3|	-1|	7|<BR>\n" );
document.write( "|0|	12|	-2|	1|	-11|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
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document.write( "Step 1: Swap row 3 and 1<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|4|	0|	3|	-1|	7|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "|3|	-1|	-2|	-1|	-4|<BR>\n" );
document.write( "|0|	12|	-2|	1|	-11|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 2: Divide row 1 by 4<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "|3|	-1|	-2|	-1|	-4|<BR>\n" );
document.write( "|0|	12|	-2|	1|	-11|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 3: Subtract (3 × row 1) from row 3<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "|0|	-1|	-4.25|	-0.25|	-9.25|<BR>\n" );
document.write( "|0|	12|	-2|	1|	-11|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 4: Swap row 4 and 2<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	12|	-2|	1|	-11|<BR>\n" );
document.write( "|0|	-1|	-4.25|	-0.25|	-9.25|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 5: Divide row 2 by 12<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	-1|	-4.25|	-0.25|	-9.25|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 6: Subtract (-1 × row 2) from row 3<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	0|	-4.417|	-0.167|	-10.167|<BR>\n" );
document.write( "|0|	9|	-1|	1|	10|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 7: Subtract (9 × row 2) from row 4<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	0|	-4.417|	-0.167|	-10.167|<BR>\n" );
document.write( "|0|	0|	0.5|	0.25|	18.25|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 8: Divide row 3 by -4.417<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	0|	1|	0.038|	2.302|<BR>\n" );
document.write( "|0|	0|	0.5|	0.25|	18.25|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 9: Subtract (0.5 × row 3) from row 4<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	0|	1|	0.038|	2.302|<BR>\n" );
document.write( "|0|	0|	0|	0.231|	17.099|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 10: Divide row 4 by 0.231<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	-0.25|	1.75|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	0|	1|	0.038|	2.302|<BR>\n" );
document.write( "|0|	0|	0|	1|	73.98|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
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document.write( "Matrix is now in row echelon form\r<BR>\n" );
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document.write( "Step 11: Subtract (-0.25 × row 4) from row 1<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	0|	20.245|<BR>\n" );
document.write( "|0|	1|	-0.167|	0.083|	-0.917|<BR>\n" );
document.write( "|0|	0|	1|	0.038|	2.302|<BR>\n" );
document.write( "|0|	0|	0|	1|	73.98|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 12: Subtract (0.083 × row 4) from row 2<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	0|	20.245|<BR>\n" );
document.write( "|0|	1|	-0.167|	0|	-7.082|<BR>\n" );
document.write( "|0|	0|	1|	0.038|	2.302|<BR>\n" );
document.write( "|0|	0|	0|	1|	73.98|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 13: Subtract (0.038 × row 4) from row 3<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0.75|	0|	20.245|<BR>\n" );
document.write( "|0|	1|	-0.167|	0|	-7.082|<BR>\n" );
document.write( "|0|	0|	1|	0|	-0.49|<BR>\n" );
document.write( "|0|	0|	0|	1|	73.98|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 14: Subtract (0.75 × row 3) from row 1<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0|	0|	20.612|<BR>\n" );
document.write( "|0|	1|	-0.167|	0|	-7.082|<BR>\n" );
document.write( "|0|	0|	1|	0|	-0.49|<BR>\n" );
document.write( "|0|	0|	0|	1|	73.98|<BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
document.write( "\n" );
document.write( "Step 15: Subtract (-0.167 × row 3) from row 2<BR>\n" );
document.write( " 		 <BR>\n" );
document.write( " 	<BR>\n" );
document.write( "|1|	0|	0|	0|	20.612|...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "|0|	1|	0|	0|	-7.163|...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "|0|	0|	1|	0|	-0.49|...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "|0|	0|	0|	1|	73.98|...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	 <BR>\n" );
document.write( " 		 \r<BR>\n" );
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document.write( "Matrix is now in reduced row echelon form\r<BR>\n" );
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document.write( "check one:\r<BR>\n" );
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document.write( "3w - x - 2y - z = -4\r<BR>\n" );
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document.write( "3* 20.612- (-7.163) - 2(-0.49)- 73.98 = -4<BR>\n" );
document.write( "61.836+7.163+0.98- 73.98 = -4<BR>\n" );
document.write( "69.979- 73.98=-4<BR>\n" );
document.write( "-4.001=-4<BR>\n" );
document.write( "-4=-4<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );