document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043156>Question 1043156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1) Write the following sets of linear equation in augumented matrix form and solve for x1, x2, and x3 using Gauss Jordan Elimination method:\r<BR>\n" );
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document.write( "(a) 2X1 + X2 - X3 = 8<BR>\n" );
document.write( "   -3X1 - X2 + 2X3= -11<BR>\n" );
document.write( "   -2X1 + X2 + 2X3= -3\r<BR>\n" );
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document.write( "(b) 3X1 - X2 + 5X3 =-2<BR>\n" );
document.write( "    2X1 + 4X2 - X3 =3<BR>\n" );
document.write( "   -4X1 + X2 + 7X3 =10\r<BR>\n" );
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document.write( "(2) Using elementary row operations investigate the consistency of the following systems.\r<BR>\n" );
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document.write( " (a) 2X1 + 4X2 - 2X3 = 0<BR>\n" );
document.write( "     3X1 + 5X2 =1\r<BR>\n" );
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document.write( " (b)  X1 - X2 + 2X3 =4<BR>\n" );
document.write( "      X1 + X3 = 6<BR>\n" );
document.write( "     2X1 - 3X2 + 5X3 =4<BR>\n" );
document.write( "     3X1 + 2X2 - X3 =1\r<BR>\n" );
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document.write( "(3) consider the system<BR>\n" );
document.write( "     X1 + 2X2 + 3X3 = a<BR>\n" );
document.write( "    2X1 + 5X2 + (a+5)X3 = -2+2a<BR>\n" );
document.write( "        - X2  + (a^2 - a)X3 = a^2 - a<BR>\n" );
document.write( "find the values of a for which the system has <BR>\n" );
document.write( "(a) No solution (b) exactly one solution (c) Infinitely many solutions.\r<BR>\n" );
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document.write( "thank you.\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 #658262 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "(1) Write the following sets of linear equation in augumented matrix form and solve for x1, x2, and x3 using Gauss Jordan Elimination method: <BR>\n" );
document.write( "(a) 2X1 + X2 - X3 = 8<BR>\n" );
document.write( "-3X1 - X2 + 2X3= -11<BR>\n" );
document.write( "-2X1 + X2 + 2X3= -3 <BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Your matrix\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	2	1	-1	8\r\n" );
document.write( "2	-3	-1	2	-11\r\n" );
document.write( "3	-2	1	2	3\r\n" );
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document.write( "Make the pivot in the 1st column by dividing the 1st row by 2\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	1	1/2	-1/2	4\r\n" );
document.write( "2	-3	-1	2	-11\r\n" );
document.write( "3	-2	1	2	3\r\n" );
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document.write( "Eliminate the 1st column\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	1	1/2	-1/2	4\r\n" );
document.write( "2	0	1/2	1/2	1\r\n" );
document.write( "3	0	2	1	11\r\n" );
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document.write( "Make the pivot in the 2nd column by dividing the 2nd row by 1/2\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	1	1/2	-1/2	4\r\n" );
document.write( "2	0	1	1	2\r\n" );
document.write( "3	0	2	1	11\r\n" );
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document.write( "Eliminate the 2nd column\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	3\r\n" );
document.write( "2	0	1	1	2\r\n" );
document.write( "3	0	0	-1	7\r\n" );
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document.write( "Find the pivot in the 3rd column in the 3rd row (inversing the sign in the whole row)\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	1	0	-1	3\r\n" );
document.write( "2	0	1	1	2\r\n" );
document.write( "3	0	0	1	-7\r\n" );
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document.write( "Eliminate the 3rd column\r\n" );
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document.write( "&#8470;	X1	X2	X3	b\r\n" );
document.write( "1	1	0	0	-4\r\n" );
document.write( "2	0	1	0	9\r\n" );
document.write( "3	0	0	1	-7\r\n" );
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document.write( "Solution set:\r\n" );
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document.write( "x1 = -4\r\n" );
document.write( "x2 = 9\r\n" );
document.write( "x3 = -7\r\n" );
document.write( "</PRE><BR>\n" );
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