document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249045>Question 249045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve this matrix equation.\r<BR>\n" );
document.write( "\n" );
document.write( "x+y=1<BR>\n" );
document.write( "4x-3y=11<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181441 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=181441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1) Convert the system \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=1%2C4x-3y=11%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=1%2C4x-3y=11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "into the augmented matrix\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C1%2C1%2C4%2C-3%2C11%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C1%2C1%2C4%2C-3%2C11%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take note that the coefficients form the first 2x2 block and the right hand values form the last column. Visually, the correspondence is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28highlight_green%281%29%2Ax%2Bhighlight_green%281%29%2Ay=highlight%281%29%2Chighlight_green%284%29%2Ax%2Bhighlight_green%28-3%29%2Ay=highlight%2811%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2Chighlight_green%281%29%2Chighlight_green%281%29%2Chighlight%281%29%2Chighlight_green%284%29%2Chighlight_green%28-3%29%2Chighlight%2811%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This conversion of notation allows us to ignore the variables (for now) since everything is based off of the numerical coefficients and right hand values.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Step 2) Row Reduction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Our next step is to row reduce the matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C1%2C1%2C4%2C-3%2C11%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C1%2C1%2C4%2C-3%2C11%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into row reduced echelon form (rref form). (Note: Solution provided by the <a  rel=nofollow HREF=\"http://www.math.odu.edu/~bogacki/lat/\">Linear Algebra Toolkit</a>)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/rref1-2.png\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Looking at the last matrix <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C3%2C1%2C0%2C2%2C0%2C1%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C1%2C0%2C2%2C0%2C1%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the last column has the values 2 and -1 in it. So this means that the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > forming the ordered pair (2,-1).  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );