document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94554>Question 94554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Matrices-and-determiminant/94544 (2007-08-26 21:09:08): I promise this is the last time I will beg for your help PLEASE HELP =I will pay you thru pay pal if I can get this answered in the next 1/2 hr. I am willing to pay PLEASE I AM DESPERate<BR>\n" );
document.write( "Solve the system of equations by the Gaussian elimination method: <BR>\n" );
document.write( "1. Solve the system of equations by the Gaussian elimination method: <BR>\n" );
document.write( "2x+y-3z=1<BR>\n" );
document.write( "3x-y+4z=6<BR>\n" );
document.write( "x+2y-z=9 <BR>\n" );
document.write( "2. Solve the system of equations by the Gaussian elimination method: <BR>\n" );
document.write( "x-y+z=17<BR>\n" );
document.write( "x+y-z=-11<BR>\n" );
document.write( "x-y-z=9 <BR>\n" );
document.write( "Again thank you in advance for your help. <BR>\n" );
document.write( "0 solutions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68895 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=68895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alright here goes the solution for your question on solving equations by the method of gaussian elimination\r<BR>\n" );
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document.write( "2x + y - 3z = 1\r<BR>\n" );
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document.write( "3x - y + 4z = 6\r<BR>\n" );
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document.write( "x + 2y - z = 9 \r<BR>\n" );
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document.write( "The given system can be written in the augmented form as: \r<BR>\n" );
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document.write( "[2  1   -3 :  1]<BR>\n" );
document.write( "[3  -1   4 :  6]<BR>\n" );
document.write( "[1  2   -1 :  9]\r<BR>\n" );
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document.write( "The operations performed are:  \r<BR>\n" );
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document.write( "We shall first interchange the first row with the third row. \r<BR>\n" );
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document.write( "[1  2   -1 :  9]<BR>\n" );
document.write( "[3  -1   4 :  6]<BR>\n" );
document.write( "[2  1   -3 :  1]\r<BR>\n" );
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document.write( "Next:  R2 - 3R1 and R3 - 2R1 are the operations which follow\r<BR>\n" );
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document.write( "[1  2   -1 :  9]<BR>\n" );
document.write( "[0  -7   7 :  -21]<BR>\n" );
document.write( "[0  -3   -1 :  -17] \r<BR>\n" );
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document.write( "R3 - R2 is the next opeartion.\r<BR>\n" );
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document.write( "[1  2   -1 :  9]<BR>\n" );
document.write( "[0  -7   7 :  -21]<BR>\n" );
document.write( "[0  4   -8 :  4] \r<BR>\n" );
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document.write( "Lets divide R2/7 and R3/4 \r<BR>\n" );
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document.write( "[1  2   -1 :  9]<BR>\n" );
document.write( "[0  -1   1 :  -3]<BR>\n" );
document.write( "[0  1   -2 :  1] \r<BR>\n" );
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document.write( "Now R3 + R2 gives us the final step\r<BR>\n" );
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document.write( "[1  2   -1 :  9]<BR>\n" );
document.write( "[0  -1   1 :  -3]<BR>\n" );
document.write( "[0  0   -1 :  -2] \r<BR>\n" );
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document.write( "From this the given system of equations reduces to: \r<BR>\n" );
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document.write( "x + 2y - z = 9 <BR>\n" );
document.write( "-y + z = -3 <BR>\n" );
document.write( "-z = - 2\r<BR>\n" );
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document.write( "Hence, the value of z can be directly found out. \r<BR>\n" );
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document.write( "==> z = 2 \r<BR>\n" );
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document.write( "now apply back substituion.\r<BR>\n" );
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document.write( "-y + z = -3 \r<BR>\n" );
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document.write( "-y + 2 = -3\r<BR>\n" );
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document.write( "-y = -3 - 2\r<BR>\n" );
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document.write( "-y = -5 \r<BR>\n" );
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document.write( "==> y = 5 \r<BR>\n" );
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document.write( "Using y and z in the first equation we find the value of x.\r<BR>\n" );
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document.write( "x + 2y - z = 9 \r<BR>\n" );
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document.write( "x + 10 - 2 = 9\r<BR>\n" );
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document.write( "x = 9 - 8 \r<BR>\n" );
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document.write( "x = 1\r<BR>\n" );
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document.write( "Hence, the solution.\r<BR>\n" );
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document.write( "===============================================================================<BR>\n" );
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document.write( "Now the second question. \r<BR>\n" );
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document.write( "The given set of equations are:  \r<BR>\n" );
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document.write( "x - y + z = 17\r<BR>\n" );
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document.write( "x + y - z = -11\r<BR>\n" );
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document.write( "x - y - z = 9 \r<BR>\n" );
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document.write( "This in the augmented form can be written as: \r<BR>\n" );
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document.write( "[1   -1     1  : 17]<BR>\n" );
document.write( "[1    1    -1  : -11]<BR>\n" );
document.write( "[1   -1    -1  : 9]\r<BR>\n" );
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document.write( "Lets perform the firts row operation that is R2 - R1 and R3- R1\r<BR>\n" );
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document.write( "[1   -1     1  : 17]<BR>\n" );
document.write( "[0   2    -2  : -28]<BR>\n" );
document.write( "[0   0    -2  : -8]\r<BR>\n" );
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document.write( "Now we divide R2/2 and R3/2 \r<BR>\n" );
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document.write( "[1   -1     1  : 17]<BR>\n" );
document.write( "[0   1    -1  : -14]<BR>\n" );
document.write( "[0   0    -1  : -4]\r<BR>\n" );
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document.write( "Thus the above augmented matrix can be written as: \r<BR>\n" );
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document.write( "x - y + z = 17 \r<BR>\n" );
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document.write( "y - z = -14 \r<BR>\n" );
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document.write( "-z = -4\r<BR>\n" );
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document.write( "This implies z = 4 \r<BR>\n" );
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document.write( "By back substitution, we find the values of y and x. \r<BR>\n" );
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document.write( "y - 4 = -14 \r<BR>\n" );
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document.write( "y = -14 + 4 \r<BR>\n" );
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document.write( "==> y = -10 \r<BR>\n" );
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document.write( "Now we find the value of x. \r<BR>\n" );
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document.write( "x - y + z = 17 \r<BR>\n" );
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document.write( "x + 10 + 4 = 17 \r<BR>\n" );
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document.write( "x + 14 = 17 \r<BR>\n" );
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document.write( "x = 17 - 14 \r<BR>\n" );
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document.write( "x = 3 \r<BR>\n" );
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document.write( "Hence, the solution.\r<BR>\n" );
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document.write( "I hope all the stpes are quite clear..\r<BR>\n" );
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document.write( "You can get back to me for an online help in math at any time of yours. \r<BR>\n" );
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document.write( "Regards\r<BR>\n" );
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document.write( "Chitra\r<BR>\n" );
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document.write( " </SPAN>\n" );
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