document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255238>Question 255238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello I am having trouble with this problem involving matrices. Can I please get your help? Thanks!<BR>\n" );
document.write( "Compute the following product. <BR>\n" );
document.write( "[ -2 10 2]  [1 6   ]=<BR>\n" );
document.write( "[-10 9 -1]  [-9 -2 ]=<BR>\n" );
document.write( "[-3 -6 10]  [10 -2 ]=<BR>\n" );
document.write( "         <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\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 #187510 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=187510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> See this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/matrix-multiplication.solver>solver</a> for more help with multiplying matrices.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the first matrix is a <font color=red>3</font> by 3 matrix and the second matrix is a 3 by <font color=green>2</font> matrix, this means that the resulting matrix will be a <font color=red>3</font> by <font color=green>2</font> matrix. The final matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the final resulting matrix will look like:\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%283%2C3%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2Cx%2Cx%2Cx%2Cx%2Cx%2Cx%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( "note: the \"x\"s are just placeholders for now\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the corresponding entries from the <font size=\"4\" color=\"red\">1st</font> row of the first matrix by the <font size=\"4\" color=\"green\">1st</font> column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"4\" color=\"red\">1st</font> row, <font size=\"4\" color=\"green\">1st</font> column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2Chighlight%28-2%29%2Chighlight%2810%29%2Chighlight%282%29%2C-10%2C9%2C-1%2C-3%2C-6%2C10%29%29%28matrix%283%2C2%2Chighlight%281%29%2C6%2Chighlight%28-9%29%2C-2%2Chighlight%2810%29%2C-2%29%29 ALIGN=MIDDLE   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=%28-2%29%2A%281%29%2B%2810%29%2A%28-9%29%2B%282%29%2A%2810%29=-2%2B-90%2B20=-72 ALIGN=MIDDLE  ALT=\"%28-2%29%2A%281%29%2B%2810%29%2A%28-9%29%2B%282%29%2A%2810%29=-2%2B-90%2B20=-72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the <font size=\"4\" color=\"red\">1st</font> row, <font size=\"4\" color=\"green\">1st</font> column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72 ALIGN=MIDDLE  ALT=\"-72\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-72%2Cx%2Cx%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-72%2Cx%2Cx%2Cx%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the corresponding entries from the <font size=\"4\" color=\"red\">1st</font> row of the first matrix by the <font size=\"4\" color=\"green\">2nd</font> column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"4\" color=\"red\">1st</font> row, <font size=\"4\" color=\"green\">2nd</font> column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2Chighlight%28-2%29%2Chighlight%2810%29%2Chighlight%282%29%2C-10%2C9%2C-1%2C-3%2C-6%2C10%29%29%28matrix%283%2C2%2C1%2Chighlight%286%29%2C-9%2Chighlight%28-2%29%2C10%2Chighlight%28-2%29%29%29 ALIGN=MIDDLE   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=%28-2%29%2A%286%29%2B%2810%29%2A%28-2%29%2B%282%29%2A%28-2%29=-12%2B-20%2B-4=-36 ALIGN=MIDDLE  ALT=\"%28-2%29%2A%286%29%2B%2810%29%2A%28-2%29%2B%282%29%2A%28-2%29=-12%2B-20%2B-4=-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the <font size=\"4\" color=\"red\">1st</font> row, <font size=\"4\" color=\"green\">2nd</font> column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36 ALIGN=MIDDLE  ALT=\"-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-72%2C-36%2Cx%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-72%2C-36%2Cx%2Cx%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "================================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the corresponding entries from the <font size=\"4\" color=\"red\">2nd</font> row of the first matrix by the <font size=\"4\" color=\"green\">1st</font> column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"4\" color=\"red\">2nd</font> row, <font size=\"4\" color=\"green\">1st</font> column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-2%2C10%2C2%2Chighlight%28-10%29%2Chighlight%289%29%2Chighlight%28-1%29%2C-3%2C-6%2C10%29%29%28matrix%283%2C2%2Chighlight%281%29%2C6%2Chighlight%28-9%29%2C-2%2Chighlight%2810%29%2C-2%29%29 ALIGN=MIDDLE   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=%28-10%29%2A%281%29%2B%289%29%2A%28-9%29%2B%28-1%29%2A%2810%29=-10%2B-81%2B-10=-101 ALIGN=MIDDLE  ALT=\"%28-10%29%2A%281%29%2B%289%29%2A%28-9%29%2B%28-1%29%2A%2810%29=-10%2B-81%2B-10=-101\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the <font size=\"4\" color=\"red\">2nd</font> row, <font size=\"4\" color=\"green\">1st</font> column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-101 ALIGN=MIDDLE  ALT=\"-101\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-72%2C-36%2C-101%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-72%2C-36%2C-101%2Cx%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the corresponding entries from the <font size=\"4\" color=\"red\">2nd</font> row of the first matrix by the <font size=\"4\" color=\"green\">2nd</font> column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"4\" color=\"red\">2nd</font> row, <font size=\"4\" color=\"green\">2nd</font> column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-2%2C10%2C2%2Chighlight%28-10%29%2Chighlight%289%29%2Chighlight%28-1%29%2C-3%2C-6%2C10%29%29%28matrix%283%2C2%2C1%2Chighlight%286%29%2C-9%2Chighlight%28-2%29%2C10%2Chighlight%28-2%29%29%29 ALIGN=MIDDLE   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=%28-10%29%2A%286%29%2B%289%29%2A%28-2%29%2B%28-1%29%2A%28-2%29=-60%2B-18%2B2=-76 ALIGN=MIDDLE  ALT=\"%28-10%29%2A%286%29%2B%289%29%2A%28-2%29%2B%28-1%29%2A%28-2%29=-60%2B-18%2B2=-76\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the <font size=\"4\" color=\"red\">2nd</font> row, <font size=\"4\" color=\"green\">2nd</font> column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-76 ALIGN=MIDDLE  ALT=\"-76\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-72%2C-36%2C-101%2C-76%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-72%2C-36%2C-101%2C-76%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "================================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the corresponding entries from the <font size=\"4\" color=\"red\">3rd</font> row of the first matrix by the <font size=\"4\" color=\"green\">1st</font> column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"4\" color=\"red\">3rd</font> row, <font size=\"4\" color=\"green\">1st</font> column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-2%2C10%2C2%2C-10%2C9%2C-1%2Chighlight%28-3%29%2Chighlight%28-6%29%2Chighlight%2810%29%29%29%28matrix%283%2C2%2Chighlight%281%29%2C6%2Chighlight%28-9%29%2C-2%2Chighlight%2810%29%2C-2%29%29 ALIGN=MIDDLE   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=%28-3%29%2A%281%29%2B%28-6%29%2A%28-9%29%2B%2810%29%2A%2810%29=-3%2B54%2B100=151 ALIGN=MIDDLE  ALT=\"%28-3%29%2A%281%29%2B%28-6%29%2A%28-9%29%2B%2810%29%2A%2810%29=-3%2B54%2B100=151\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the <font size=\"4\" color=\"red\">3rd</font> row, <font size=\"4\" color=\"green\">1st</font> column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=151 ALIGN=MIDDLE  ALT=\"151\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-72%2C-36%2C-101%2C-76%2C151%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-72%2C-36%2C-101%2C-76%2C151%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the corresponding entries from the <font size=\"4\" color=\"red\">3rd</font> row of the first matrix by the <font size=\"4\" color=\"green\">2nd</font> column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font size=\"4\" color=\"red\">3rd</font> row, <font size=\"4\" color=\"green\">2nd</font> column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-2%2C10%2C2%2C-10%2C9%2C-1%2Chighlight%28-3%29%2Chighlight%28-6%29%2Chighlight%2810%29%29%29%28matrix%283%2C2%2C1%2Chighlight%286%29%2C-9%2Chighlight%28-2%29%2C10%2Chighlight%28-2%29%29%29 ALIGN=MIDDLE   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=%28-3%29%2A%286%29%2B%28-6%29%2A%28-2%29%2B%2810%29%2A%28-2%29=-18%2B12%2B-20=-26 ALIGN=MIDDLE  ALT=\"%28-3%29%2A%286%29%2B%28-6%29%2A%28-2%29%2B%2810%29%2A%28-2%29=-18%2B12%2B-20=-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the <font size=\"4\" color=\"red\">3rd</font> row, <font size=\"4\" color=\"green\">2nd</font> column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-26 ALIGN=MIDDLE  ALT=\"-26\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-72%2C-36%2C-101%2C-76%2C151%2C-26%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C-72%2C-36%2C-101%2C-76%2C151%2C-26%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==============================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solution is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C2%2C-72%2C-36%2C-101%2C-76%2C151%2C-26%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C2%2C-72%2C-36%2C-101%2C-76%2C151%2C-26%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C-2%2C10%2C2%2C-10%2C9%2C-1%2C-3%2C-6%2C10%29%29%2A%28matrix%283%2C3%2C1%2C6%2C-9%2C-2%2C10%2C-2%29%29=%28matrix%283%2C2%2C-72%2C-36%2C-101%2C-76%2C151%2C-26%29%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( "Once again, see this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/matrix-multiplication.solver>solver</a> for more help with multiplying matrices. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );