document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126342>Question 126342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse(if it exists)\r<BR>\n" );
document.write( "\n" );
document.write( "1  0  1<BR>\n" );
document.write( "1  1 -3<BR>\n" );
document.write( "0  1 -3\r<BR>\n" );
document.write( "\n" );
document.write( "i don't know how to solve a 3x3 if you can please explain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92539 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For an n X n matrix, create an n X 2n matrix by adding n columns consisting of the n X n identity matrix.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your problem:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28matrix%283%2C3%2C%0D%0A1%2C0%2C1%2C%0D%0A1%2C1%2C-3%2C%0D%0A0%2C1%2C-3%29%29 ALIGN=MIDDLE  ALT=\"A=%28matrix%283%2C3%2C%0D%0A1%2C0%2C1%2C%0D%0A1%2C1%2C-3%2C%0D%0A0%2C1%2C-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The 3 X 3 Identity matrix:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C%0D%0A1%2C0%2C0%2C%0D%0A0%2C1%2C0%2C%0D%0A0%2C0%2C1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C%0D%0A1%2C0%2C0%2C%0D%0A0%2C1%2C0%2C%0D%0A0%2C0%2C1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Putting them together in a 3 X 6 matrix:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+1%2C+1%2C+0%2C+0%2C%0D%0A1%2C+1%2C-3%2C+0%2C+1%2C+0%2C%0D%0A0%2C+1%2C-3%2C+0%2C+0%2C+1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, perform row reduction operations until the matrix is completely reduced, if possible.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R2+=+R2+-+R1 ALIGN=MIDDLE  ALT=\"R2+=+R2+-+R1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+1%2C+1%2C+0%2C+0%2C%0D%0A0%2C+1%2C-4%2C-1%2C+1%2C+0%2C%0D%0A0%2C+1%2C-3%2C+0%2C+0%2C+1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\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=R3+=+R3+-+R2 ALIGN=MIDDLE  ALT=\"R3+=+R3+-+R2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+1%2C+1%2C+0%2C+0%2C%0D%0A0%2C+1%2C-4%2C-1%2C+1%2C+0%2C%0D%0A0%2C+0%2C+1%2C+1%2C-1%2C+1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R1+=+R1+-+R3 ALIGN=MIDDLE  ALT=\"R1+=+R1+-+R3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+0%2C+0%2C+1%2C-1%2C%0D%0A0%2C+1%2C-4%2C-1%2C+1%2C+0%2C%0D%0A0%2C+0%2C+1%2C+1%2C-1%2C+1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R2+=+R2+%2B+4R3 ALIGN=MIDDLE  ALT=\"R2+=+R2+%2B+4R3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C6%2C%0D%0A1%2C+0%2C+0%2C+0%2C+1%2C-1%2C%0D%0A0%2C+1%2C+0%2C+3%2C-3%2C+4%2C%0D%0A0%2C+0%2C+1%2C+1%2C-1%2C+1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E%28-1%29=%28matrix%283%2C3%2C%0D%0A0%2C+1%2C-1%2C%0D%0A3%2C-3%2C+4%2C%0D%0A1%2C-1%2C+1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );