document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182077>Question 182077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Matrices<BR>\n" );
document.write( "Hello I'm needing some help with my homework that asks me to use the matrices to solve each system of equations. If a system has no solution, so indicate. \r<BR>\n" );
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document.write( "{x-y+z=2<BR>\n" );
document.write( " x+2y-z=6<BR>\n" );
document.write( " 2x-y-z=3\r<BR>\n" );
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document.write( "thanks\r<BR>\n" );
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document.write( "Haley </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136668 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> |x - y + z  2|<BR>\n" );
document.write( "|x +2y - z  6| = 0<BR>\n" );
document.write( "|2x -y - z  3|<BR>\n" );
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document.write( "You can leave out the x, y and z.<BR>\n" );
document.write( "|1 -1  +1 2|<BR>\n" );
document.write( "|1 +2 -1 6| = 0<BR>\n" );
document.write( "|2 -1 -1 3|<BR>\n" );
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document.write( "First, find the determinant.<BR>\n" );
document.write( "DET = 1*(-2-1) + 1*(-1+2) + 1*(-1-4) = -3+1-5<BR>\n" );
document.write( "DET = -7<BR>\n" );
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document.write( "x*DET = -1(-3+6) -1(6+6) +2(-2-1) =-3-12-6 = -21<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "-y*DET = 1(-3+6) -1(3-12) +2(-1+2) = 3+9+2 = 14<BR>\n" );
document.write( "y = 2<BR>\n" );
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document.write( "At this point, I'd substitute to find z, but it says use a matrix.<BR>\n" );
document.write( "z*DET = 1(6+6) +1(3-12) +2(-1-4) = 12-9-10 = -7<BR>\n" );
document.write( "z = 1<BR>\n" );
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document.write( "You can find solvers online to do these, or you can do them with an Excel sheet. </SPAN>\n" );
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