document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150173>Question 150173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this using matrices:<BR>\n" );
document.write( "x + 2y - z = 2<BR>\n" );
document.write( "2x - 2y + z = -1<BR>\n" );
document.write( "6x +4y +3z = 5<BR>\n" );
document.write( "Thank you so much, Lennie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110203 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In Matrix notation, the problem is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A++matrix%28+3%2C+3%2C+%0D%0A++++1%2C+2%2C+-1%2C%0D%0A++++2%2C+-2%2C+1%2C%0D%0A++++6%2C+4%2C+3%0D%0A++%29%29%2A%0D%0A%28%0D%0A++matrix%28+3%2C+1%2C+%0D%0A++++x%2C+%0D%0A++++y%2C+%0D%0A++++z%0D%0A++%29%0D%0A%29=%0D%0A%28%0D%0A++matrix%28+3%2C+1%2C+%0D%0A++++2%2C+%0D%0A++++-1%2C+%0D%0A++++5%0D%0A++%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or simplified<BR>\n" );
document.write( "[A][x]=[b]<BR>\n" );
document.write( "[Ainv][A][x]=[Ainv][b]<BR>\n" );
document.write( "[x]=[Ainv][b]<BR>\n" );
document.write( "Find the inverse of matrix A, multiply by the right hand side to find the solution.<BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "[A]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A++matrix%28+3%2C+3%2C+%0D%0A++++1%2C+2%2C+-1%2C%0D%0A++++2%2C+-2%2C+1%2C%0D%0A++++6%2C+4%2C+3%0D%0A++%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The inverse of [A] is, <BR>\n" );
document.write( "[Ainv]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F30%29%2A%28%0D%0A++matrix%28+3%2C+3%2C+%0D%0A++++10%2C+10%2C+0%2C%0D%0A++++0%2C+-9%2C+3%2C%0D%0A++++-20%2C+-8%2C+6%0D%0A++%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then the matrix multiplication is,<BR>\n" );
document.write( "[x]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F14%29%2A%28%0D%0A++matrix%28+3%2C+3%2C+%0D%0A++++10%2C+10%2C+0%2C%0D%0A++++0%2C+-9%2C+3%2C%0D%0A++++-20%2C+-8%2C+6%0D%0A++%29%29%2A%28%0D%0A++matrix%28+3%2C+1%2C+%0D%0A++++2%2C+%0D%0A++++-1%2C+%0D%0A++++5%0D%0A++%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F30%29%2810%2A2%2B%2810%29%28-1%29%2B0%285%29%29 ALIGN=MIDDLE  ALT=\"x=%281%2F30%29%2810%2A2%2B%2810%29%28-1%29%2B0%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F30%29%2820-10%29 ALIGN=MIDDLE  ALT=\"x=%281%2F30%29%2820-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2F30%29%2810%29 ALIGN=MIDDLE  ALT=\"x=%281%2F30%29%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F30%29%280%2A2%2B%28-9%29%28-1%29%2B%283%29%285%29%29 ALIGN=MIDDLE  ALT=\"y=%281%2F30%29%280%2A2%2B%28-9%29%28-1%29%2B%283%29%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F30%29%289%2B15%29 ALIGN=MIDDLE  ALT=\"y=%281%2F30%29%289%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F30%29%2824%29 ALIGN=MIDDLE  ALT=\"y=%281%2F30%29%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2F5 ALIGN=MIDDLE  ALT=\"y=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%281%2F30%29%2820%2A2%2B%288%29%28-1%29%2B%28-6%29%285%29%29 ALIGN=MIDDLE  ALT=\"z=%281%2F30%29%2820%2A2%2B%288%29%28-1%29%2B%28-6%29%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%281%2F30%29%2840-8-30%29 ALIGN=MIDDLE  ALT=\"z=%281%2F30%29%2840-8-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%281%2F30%29%282%29 ALIGN=MIDDLE  ALT=\"z=%281%2F30%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-1%2F15 ALIGN=MIDDLE  ALT=\"z=-1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your solution matrix is then<BR>\n" );
document.write( "[x]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%0D%0A++matrix%28+3%2C+1%2C+%0D%0A++++1%2F3%2C+%0D%0A++++4%2F5%2C+%0D%0A++++-1%2F15%0D%0A++%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );