document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=292657>Question 292657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiplying matrics\r<BR>\n" );
document.write( "\n" );
document.write( "[4 1 0 2] 1 0 1<BR>\n" );
document.write( "          2 -1 0<BR>\n" );
document.write( "          3  5 1<BR>\n" );
document.write( "          1  3 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211361 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211361\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%281%2C4%2C%0D%0A4%2C+1%2C+0%2C+2%29%29%2A%0D%0A%0D%0A%28matrix%284%2C3%2C+%0D%0A%0D%0A%0D%0A1%2C+0%2C+1%2C%0D%0A2%2C+-1%2C+0%2C%0D%0A3%2C++5%2C+1%2C%0D%0A1%2C++3%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "This is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%284%29 ALIGN=MIDDLE  ALT=\"green%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > matrix multiplied by a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%284%29 ALIGN=MIDDLE  ALT=\"green%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "The multiplication is defined because the two (green) inner <BR>\n" );
document.write( "dimensions are both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%284%29 ALIGN=MIDDLE  ALT=\"green%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the product matrix will <BR>\n" );
document.write( "have the outer (red) dimensions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%29 ALIGN=MIDDLE  ALT=\"red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%283%29 ALIGN=MIDDLE  ALT=\"red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
document.write( "\n" );
document.write( "So we make a blank <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > matrix to fill in:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%281%2C4%2C%0D%0A4%2C+1%2C+0%2C+2%29%29%2A%0D%0A%0D%0A%28matrix%284%2C3%2C+%0D%0A%0D%0A%0D%0A1%2C+0%2C+1%2C%0D%0A2%2C+-1%2C+0%2C%0D%0A3%2C++5%2C+1%2C%0D%0A1%2C++3%2C+0%29%29+%0D%0A%0D%0A=%0D%0A%0D%0A%28matrix%281%2C3%2C%22_%22%2C%22_%22%2C%22_%22%29%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The first element to fill in is the 1st (only) row and 1st column.\r<BR>\n" );
document.write( "\n" );
document.write( "So we multiply the first (only) row of the first matrix by the<BR>\n" );
document.write( "first column of the second matrix and then add them like this:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A1+%2B+1%2A2+%2B+0%2A3+%2B+2%2A1+=+4+%2B+2+%2B+0+%2B+2+=+8 ALIGN=MIDDLE  ALT=\"4%2A1+%2B+1%2A2+%2B+0%2A3+%2B+2%2A1+=+4+%2B+2+%2B+0+%2B+2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "we put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%288%29 ALIGN=MIDDLE  ALT=\"red%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the first blank of the product matrix:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%281%2C4%2C%0D%0A4%2C+1%2C+0%2C+2%29%29%2A%0D%0A%0D%0A%28matrix%284%2C3%2C+%0D%0A%0D%0A%0D%0A1%2C+0%2C+1%2C%0D%0A2%2C+-1%2C+0%2C%0D%0A3%2C++5%2C+1%2C%0D%0A1%2C++3%2C+0%29%29+%0D%0A%0D%0A=%0D%0A%0D%0A%28matrix%281%2C3%2Cred%288%29%2C%22_%22%2C%22_%22%29%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The second element to fill in is the 1st (only) row and 2nd column.\r<BR>\n" );
document.write( "\n" );
document.write( "So we multiply the first (only) row of the first matrix by the<BR>\n" );
document.write( "2nd column of the second matrix and then add them like this:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A0+%2B+1%2A%28-1%29+%2B+0%2A5+%2B+2%2A3+=+0+-+1+%2B+0+%2B+6+=+5 ALIGN=MIDDLE  ALT=\"4%2A0+%2B+1%2A%28-1%29+%2B+0%2A5+%2B+2%2A3+=+0+-+1+%2B+0+%2B+6+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "we put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%285%29 ALIGN=MIDDLE  ALT=\"red%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the second blank of the product matrix:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%281%2C4%2C%0D%0A4%2C+1%2C+0%2C+2%29%29%2A%0D%0A%0D%0A%28matrix%284%2C3%2C+%0D%0A%0D%0A%0D%0A1%2C+0%2C+1%2C%0D%0A2%2C+-1%2C+0%2C%0D%0A3%2C++5%2C+1%2C%0D%0A1%2C++3%2C+0%29%29+%0D%0A%0D%0A=%0D%0A%0D%0A%28matrix%281%2C3%2Cred%288%29%2Cred%285%29%2C%22_%22%29%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "The third element to fill in is the 1st (only) row and 3rd column.\r<BR>\n" );
document.write( "\n" );
document.write( "So we multiply the first (only) row of the first matrix by the<BR>\n" );
document.write( "3rd column of the second matrix and then add them like this:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A1+%2B+1%2A0+%2B+0%2A1+%2B+2%2A0+=+4+%2B+0+%2B+0+%2B+0+=+4 ALIGN=MIDDLE  ALT=\"4%2A1+%2B+1%2A0+%2B+0%2A1+%2B+2%2A0+=+4+%2B+0+%2B+0+%2B+0+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "we put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%284%29 ALIGN=MIDDLE  ALT=\"red%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the third blank of the product matrix:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%281%2C4%2C%0D%0A4%2C+1%2C+0%2C+2%29%29%2A%0D%0A%0D%0A%28matrix%284%2C3%2C+%0D%0A%0D%0A%0D%0A1%2C+0%2C+1%2C%0D%0A2%2C+-1%2C+0%2C%0D%0A3%2C++5%2C+1%2C%0D%0A1%2C++3%2C+0%29%29+%0D%0A%0D%0A=%0D%0A%0D%0A%28matrix%281%2C3%2Cred%288%29%2Cred%285%29%2Cred%284%29%29%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );