document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176531>Question 176531</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is BA: B=[2, 8, .6, 3] A=[3, 0, 2, -1] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131628 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=131628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that the matrices are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29 ALIGN=MIDDLE  ALT=\"B=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"A=%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29\"   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=BA ALIGN=MIDDLE  ALT=\"BA\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29 ALIGN=MIDDLE  ALT=\"B=%28matrix%282%2C2%2C2%2C8%2C0.6%2C3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"A=%28matrix%282%2C2%2C3%2C0%2C2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the first matrix is a 2 by 2 matrix and the second matrix is a 2 by 2 matrix, this means that the resulting matrix will be a 2 by  2 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 1st row of the first matrix by the 1st column of the second matrix. After multiplying, add the values:\r<BR>\n" );
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document.write( "1st row, 1st column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%288%29%2C0.6%2C3%29%29%28matrix%282%2C2%2Chighlight%283%29%2C0%2Chighlight%282%29%2C-1%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%283%29%2B%288%29%2A%282%29=6%2B16=22 ALIGN=MIDDLE  ALT=\"%282%29%2A%283%29%2B%288%29%2A%282%29=6%2B16=22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " So the element in the 1st row, 1st column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22 ALIGN=MIDDLE  ALT=\"22\"   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 1st row of the first matrix by the 2nd column of the second matrix. After multiplying, add the values:\r<BR>\n" );
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document.write( "1st row, 2nd column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%288%29%2C0.6%2C3%29%29%28matrix%282%2C2%2C3%2Chighlight%280%29%2C2%2Chighlight%28-1%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%280%29%2B%288%29%2A%28-1%29=0%2B-8=-8 ALIGN=MIDDLE  ALT=\"%282%29%2A%280%29%2B%288%29%2A%28-1%29=0%2B-8=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " So the element in the 1st row, 2nd column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   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 2nd row of the first matrix by the 1st column of the second matrix. After multiplying, add the values:\r<BR>\n" );
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document.write( "2nd row, 1st column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C8%2Chighlight%280.6%29%2Chighlight%283%29%29%29%28matrix%282%2C2%2Chighlight%283%29%2C0%2Chighlight%282%29%2C-1%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=%280.6%29%2A%283%29%2B%283%29%2A%282%29=1.8%2B6=7.8 ALIGN=MIDDLE  ALT=\"%280.6%29%2A%283%29%2B%283%29%2A%282%29=1.8%2B6=7.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " So the element in the 2nd row, 1st column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.8 ALIGN=MIDDLE  ALT=\"7.8\"   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 2nd row of the first matrix by the 2nd column of the second matrix. After multiplying, add the values:\r<BR>\n" );
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document.write( "2nd row, 2nd column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C8%2Chighlight%280.6%29%2Chighlight%283%29%29%29%28matrix%282%2C2%2C3%2Chighlight%280%29%2C2%2Chighlight%28-1%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=%280.6%29%2A%280%29%2B%283%29%2A%28-1%29=0%2B-3=-3 ALIGN=MIDDLE  ALT=\"%280.6%29%2A%280%29%2B%283%29%2A%28-1%29=0%2B-3=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " So the element in the 2nd row, 2nd column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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%2C22%2C-8%2C7.8%2C-3%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C22%2C-8%2C7.8%2C-3%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( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BA=%28matrix%282%2C2%2C22%2C-8%2C7.8%2C-3%29%29 ALIGN=MIDDLE  ALT=\"BA=%28matrix%282%2C2%2C22%2C-8%2C7.8%2C-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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