document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29946>Question 29946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am so confused as to how to figured out a matrix problem using the Gauss-Jordan Method.<BR>\n" );
document.write( "Problem:<BR>\n" );
document.write( "3X-2Y=-8Z+9<BR>\n" );
document.write( "-2X+Z=-2Y+3<BR>\n" );
document.write( "2Y-3Z+X=8\r<BR>\n" );
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document.write( "Thanks!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18004 by </B><A HREF=/tutors/aboutme.mpl?userid=brianunlv><B>brianunlv(12)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=brianunlv><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.nevada.edu/~dadevitt/brianbird.htm valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> system of equations we have:<BR>\n" );
document.write( "+3x - 2y + 8z = 9<BR>\n" );
document.write( "-2x + 2y + z = 3<BR>\n" );
document.write( " +x + 2y - 37 = 8<BR>\n" );
document.write( "in equation form:<BR>\n" );
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document.write( "|3 -2 8 |x|`|9|<BR>\n" );
document.write( "|-2 2 1 |y|=|3|<BR>\n" );
document.write( "|1 2 -3 |z|`|8|<BR>\n" );
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document.write( "in matrix form:<BR>\n" );
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document.write( "|3 -2 8 |9||x|<BR>\n" );
document.write( "|-2 2 1 |3||y|<BR>\n" );
document.write( "|1 2 -3 |8||z|<BR>\n" );
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document.write( "first do gauss elemination (bottum left triangle = 0):<BR>\n" );
document.write( "1.switch row1(R1) with row3(R3):<BR>\n" );
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document.write( "|1 2 -3 |8||x|<BR>\n" );
document.write( "|-2 2 1 |3||y|<BR>\n" );
document.write( "|3 -2 8 |9||z|<BR>\n" );
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document.write( "2.subtract 3*(R1) from (R3):<BR>\n" );
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document.write( "|1 2 -3 |8||x|<BR>\n" );
document.write( "|-2 2 1 |3||y|<BR>\n" );
document.write( "|0 -8 17 |-15||z|<BR>\n" );
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document.write( "3.subtract -4*(R1) from (R3):<BR>\n" );
document.write( "-<BR>\n" );
document.write( "|1 2 -3 |8||x|<BR>\n" );
document.write( "|-2 2 1 |3||y|<BR>\n" );
document.write( "|0 0 5 |9||z|--->we can see z = 9/5 already<BR>\n" );
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document.write( "4.subtract -2*(R1) from (R2):<BR>\n" );
document.write( "-<BR>\n" );
document.write( "|1 2 -3 |8||x|<BR>\n" );
document.write( "|0 6 -5 |19||y|<BR>\n" );
document.write( "|0 0 5 |9||z|<BR>\n" );
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document.write( "Now do jordan elemination (top right triangle = 0):<BR>\n" );
document.write( "1. subtract -5/3*(R1) from (R2):<BR>\n" );
document.write( "-<BR>\n" );
document.write( "|1 2 -3 |8||x|<BR>\n" );
document.write( "|0 6 0 |97/3||y|--->we can see y = (97/3)/6 already<BR>\n" );
document.write( "|0 0 5 |9||z|<BR>\n" );
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document.write( "2. So we can now find x with back substitution:<BR>\n" );
document.write( " x + 2((97/3)/6) - 3(9/5) = 8<BR>\n" );
document.write( " x + (1164/3) - (27/5) = 8<BR>\n" );
document.write( "x + 382 3/5 = 8<BR>\n" );
document.write( "x = 8 - 382 3/5<BR>\n" );
document.write( "x = 374 3/5\r<BR>\n" );
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document.write( "Regards,<BR>\n" );
document.write( "Brian Bird\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );