document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347423>Question 347423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the product of \r<BR>\n" );
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document.write( "2 3 5     <BR>\n" );
document.write( "0 1 2 <BR>\n" );
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document.write( "x \r<BR>\n" );
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document.write( "4  2<BR>\n" );
document.write( "-1 0<BR>\n" );
document.write( "-3 2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248417 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=248417\">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" );
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document.write( "Since the first matrix is a <font color=red>2</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>2</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" );
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document.write( "So the final resulting matrix will look like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Cx%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2Cx%2Cx%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "note: the \"x\"s are just placeholders for now\r<BR>\n" );
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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" );
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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%282%2C3%2Chighlight%282%29%2Chighlight%283%29%2Chighlight%285%29%2C0%2C1%2C2%29%29%28matrix%283%2C2%2Chighlight%284%29%2C2%2Chighlight%28-1%29%2C0%2Chighlight%28-3%29%2C2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2A%284%29%2B%283%29%2A%28-1%29%2B%285%29%2A%28-3%29=8%2B-3%2B-15=-10 ALIGN=MIDDLE  ALT=\"%282%29%2A%284%29%2B%283%29%2A%28-1%29%2B%285%29%2A%28-3%29=8%2B-3%2B-15=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=-10 ALIGN=MIDDLE  ALT=\"-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
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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" );
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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%282%2C3%2Chighlight%282%29%2Chighlight%283%29%2Chighlight%285%29%2C0%2C1%2C2%29%29%28matrix%283%2C2%2C4%2Chighlight%282%29%2C-1%2Chighlight%280%29%2C-3%2Chighlight%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2A%282%29%2B%283%29%2A%280%29%2B%285%29%2A%282%29=4%2B0%2B10=14 ALIGN=MIDDLE  ALT=\"%282%29%2A%282%29%2B%283%29%2A%280%29%2B%285%29%2A%282%29=4%2B0%2B10=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
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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" );
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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%282%2C3%2C2%2C3%2C5%2Chighlight%280%29%2Chighlight%281%29%2Chighlight%282%29%29%29%28matrix%283%2C2%2Chighlight%284%29%2C2%2Chighlight%28-1%29%2C0%2Chighlight%28-3%29%2C2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%2A%284%29%2B%281%29%2A%28-1%29%2B%282%29%2A%28-3%29=0%2B-1%2B-6=-7 ALIGN=MIDDLE  ALT=\"%280%29%2A%284%29%2B%281%29%2A%28-1%29%2B%282%29%2A%28-3%29=0%2B-1%2B-6=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C-10%2C14%2C-7%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C-10%2C14%2C-7%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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" );
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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%282%2C3%2C2%2C3%2C5%2Chighlight%280%29%2Chighlight%281%29%2Chighlight%282%29%29%29%28matrix%283%2C2%2C4%2Chighlight%282%29%2C-1%2Chighlight%280%29%2C-3%2Chighlight%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%2A%282%29%2B%281%29%2A%280%29%2B%282%29%2A%282%29=0%2B0%2B4=4 ALIGN=MIDDLE  ALT=\"%280%29%2A%282%29%2B%281%29%2A%280%29%2B%282%29%2A%282%29=0%2B0%2B4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C-10%2C14%2C-7%2C4%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C-10%2C14%2C-7%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words,\r<BR>\n" );
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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.\r<BR>\n" );
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