document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138333>Question 138333</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131491040/algebrahomeworkh>College Algebra Enhanced With Graphing Utilities</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The question asks:<BR>\n" );
document.write( "Solve each system of equations using matrices (row operations).\r<BR>\n" );
document.write( "\n" );
document.write( "Problem 49:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y%2B3z=7 ALIGN=MIDDLE  ALT=\"x-2y%2B3z=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2By%2Bz=4 ALIGN=MIDDLE  ALT=\"2x%2By%2Bz=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2B2y-2z=-10 ALIGN=MIDDLE  ALT=\"-3x%2B2y-2z=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's what I've tried:<BR>\n" );
document.write( "Original augmented matrix:<BR>\n" );
document.write( "[1 -2 3 7]<BR>\n" );
document.write( "[2 1 1 4]<BR>\n" );
document.write( "[-3 2 -2 -10]\r<BR>\n" );
document.write( "\n" );
document.write( "*R[3]=r[1]+r[3]<BR>\n" );
document.write( "[1 -2 3 7]<BR>\n" );
document.write( "[2 1 1 4]<BR>\n" );
document.write( "[-2 0 1 -3]\r<BR>\n" );
document.write( "\n" );
document.write( "*R[2]=-2r[1]+r[2]<BR>\n" );
document.write( "*R[3]=2r[1]+r[3]<BR>\n" );
document.write( "[1 -2 3 7]<BR>\n" );
document.write( "[0 5 -5 -10]<BR>\n" );
document.write( "[0 -4 7 11]\r<BR>\n" );
document.write( "\n" );
document.write( "*R[2]=(1/5)r[2]<BR>\n" );
document.write( "*R[3]=-2r[1]+r[3]<BR>\n" );
document.write( "[1 -2 3 7]<BR>\n" );
document.write( "[0 1 -1 -2]<BR>\n" );
document.write( "[0 0 1 -3]\r<BR>\n" );
document.write( "\n" );
document.write( "*R[1]=2r[2]+r[1]<BR>\n" );
document.write( "[1 0 1 3]<BR>\n" );
document.write( "[0 1 -1 -2]<BR>\n" );
document.write( "[0 0 1 -3]\r<BR>\n" );
document.write( "\n" );
document.write( "*R[1]=-1r[3]+r[1]<BR>\n" );
document.write( "[1 0 0 6]<BR>\n" );
document.write( "[0 1 -1 -2]<BR>\n" );
document.write( "[0 0 1 -3]\r<BR>\n" );
document.write( "\n" );
document.write( "*R[2]=r[3]+r[2]<BR>\n" );
document.write( "[1 0 0 6]<BR>\n" );
document.write( "[0 1 0 -5]<BR>\n" );
document.write( "[0 0 1 -3]\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, I assume that the answer is x=6, y=-5, z=-3<BR>\n" );
document.write( "BUT it's not.  The answer is actually x=2, y=-1, z=1<BR>\n" );
document.write( "When I input the matrix into my TI 84 Plus, I get<BR>\n" );
document.write( "[1 0 0 2]<BR>\n" );
document.write( "[0 1 0 -1]<BR>\n" );
document.write( "[0 0 1 1]<BR>\n" );
document.write( "which is the correct answer.\r<BR>\n" );
document.write( "\n" );
document.write( "So, I know the start, I know the end, but I'm having trouble with the innards.  Any suggestions?  Thanks in advance for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101023 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve each system of equations using matrices (row operations). <BR>\n" );
document.write( "Problem 49:<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "Here's what I've tried:<BR>\n" );
document.write( "Original augmented matrix:<BR>\n" );
document.write( "[1 -2  3   7]<BR>\n" );
document.write( "[2  1  1   4]<BR>\n" );
document.write( "[-3 2 -2 -10] <BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "*R[3]=r[1]+r[3]<BR>\n" );
document.write( "[ 1 -2 3  7]<BR>\n" );
document.write( "[ 2  1 1  4]<BR>\n" );
document.write( "[-2  0 1 -3]<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "*R[2]=-2r[1]+r[2]<BR>\n" );
document.write( "*R[3]=2r[1]+r[3]<BR>\n" );
document.write( "[1 -2 3 7]<BR>\n" );
document.write( "[0 5 -5 -10]<BR>\n" );
document.write( "[0 -4 7 11] <BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "*R[2]=(1/5)r[2]<BR>\n" );
document.write( "*R[3]=-2r[1]+r[3]<BR>\n" );
document.write( "[1 -2 3 7]<BR>\n" );
document.write( "[0 1 -1 -2]<BR>\n" );
document.write( "[0 0 1 -3] <BR>\n" );
document.write( "You made an error in forming R[3}<BR>\n" );
document.write( "You should leave r(1)alone and work r(2) against r(3)<BR>\n" );
document.write( "I would suggest you not try to do 2 steps in one transformation of the matrix.\r<BR>\n" );
document.write( "\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "*R[1]=2r[2]+r[1]<BR>\n" );
document.write( "[1 0 1 3]<BR>\n" );
document.write( "[0 1 -1 -2]<BR>\n" );
document.write( "[0 0 1 -3] <BR>\n" );
document.write( "*R[1]=-1r[3]+r[1]<BR>\n" );
document.write( "[1 0 0 6]<BR>\n" );
document.write( "[0 1 -1 -2]<BR>\n" );
document.write( "[0 0 1 -3] <BR>\n" );
document.write( "*R[2]=r[3]+r[2]<BR>\n" );
document.write( "[1 0 0 6]<BR>\n" );
document.write( "[0 1 0 -5]<BR>\n" );
document.write( "[0 0 1 -3] <BR>\n" );
document.write( "Therefore, I assume that the answer is x=6, y=-5, z=-3<BR>\n" );
document.write( "BUT it's not. The answer is actually x=2, y=-1, z=1<BR>\n" );
document.write( "When I input the matrix into my TI 84 Plus, I get<BR>\n" );
document.write( "[1 0 0 2]<BR>\n" );
document.write( "[0 1 0 -1]<BR>\n" );
document.write( "[0 0 1 1]<BR>\n" );
document.write( "which is the correct answer. <BR>\n" );
document.write( "So, I know the start, I know the end, but I'm having trouble with the innards. Any suggestions? Thanks in advance for your help!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );