document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200366>Question 200366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi everyone I asked a similiar question recently but got no responce, I may have input the question incorrectly.<BR>\n" );
document.write( "I  need to solve the following Matrices and comment on the outcomes.<BR>\n" );
document.write( "For the following:<BR>\n" );
document.write( "A =  <BR>\n" );
document.write( "( 1  0 )<BR>\n" );
document.write( "  0  1 \r<BR>\n" );
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document.write( "B =  <BR>\n" );
document.write( "( 2  1 ) <BR>\n" );
document.write( "   3  2 \r<BR>\n" );
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document.write( "C =  <BR>\n" );
document.write( "( 1  4 )<BR>\n" );
document.write( "  3 -1<BR>\n" );
document.write( " -2  5<BR>\n" );
document.write( " <BR>\n" );
document.write( "Find and state why or why not the following is possible.<BR>\n" );
document.write( "i) AB<BR>\n" );
document.write( "ii) B^1<BR>\n" );
document.write( "iii) BC^T </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150703 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=150703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i)\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%281%29%2Chighlight%280%29%2C0%2C1%29%29%28matrix%282%2C2%2Chighlight%282%29%2C1%2Chighlight%283%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=%281%29%2A%282%29%2B%280%29%2A%283%29=2%2B0=2 ALIGN=MIDDLE  ALT=\"%281%29%2A%282%29%2B%280%29%2A%283%29=2%2B0=2\"   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=2 ALIGN=MIDDLE  ALT=\"2\"   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%2C2%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C2%2Cx%2Cx%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 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%281%29%2Chighlight%280%29%2C0%2C1%29%29%28matrix%282%2C2%2C2%2Chighlight%281%29%2C3%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=%281%29%2A%281%29%2B%280%29%2A%282%29=1%2B0=1 ALIGN=MIDDLE  ALT=\"%281%29%2A%281%29%2B%280%29%2A%282%29=1%2B0=1\"   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=1 ALIGN=MIDDLE  ALT=\"1\"   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%2C2%2C1%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C2%2C1%2Cx%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 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%2C1%2C0%2Chighlight%280%29%2Chighlight%281%29%29%29%28matrix%282%2C2%2Chighlight%282%29%2C1%2Chighlight%283%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%282%29%2B%281%29%2A%283%29=0%2B3=3 ALIGN=MIDDLE  ALT=\"%280%29%2A%282%29%2B%281%29%2A%283%29=0%2B3=3\"   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=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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C1%2C3%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C2%2C1%2C3%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 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%2C1%2C0%2Chighlight%280%29%2Chighlight%281%29%29%29%28matrix%282%2C2%2C2%2Chighlight%281%29%2C3%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%281%29%2B%281%29%2A%282%29=0%2B2=2 ALIGN=MIDDLE  ALT=\"%280%29%2A%281%29%2B%281%29%2A%282%29=0%2B2=2\"   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=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now let's update the matrix:\r<BR>\n" );
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document.write( "==============================================================================\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%2C2%2C1%2C3%2C2%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C2%2C1%2C3%2C2%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=%28matrix%282%2C2%2C1%2C0%2C0%2C1%29%29%2A%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29=%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29 ALIGN=MIDDLE  ALT=\"AB=%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ii)\r<BR>\n" );
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document.write( "If you raise ANY matrix to a power of 1, you'll get that same matrix as a result. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5E1=B=%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29 ALIGN=MIDDLE  ALT=\"B%5E1=B=%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "iii)\r<BR>\n" );
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document.write( "First, let's calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5ET ALIGN=MIDDLE  ALT=\"C%5ET\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the transpose of matrix C). So simply swap each row and column to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5ET=%28matrix%283%2C2%2C1%2C4%2C3%2C-1%2C-2%2C5%29%29%5ET=%28matrix%282%2C3%2C1%2C3%2C-2%2C4%2C-1%2C5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5ET=%28matrix%282%2C3%2C1%2C3%2C-2%2C4%2C-1%2C5%29%29 ALIGN=MIDDLE  ALT=\"C%5ET=%28matrix%282%2C3%2C1%2C3%2C-2%2C4%2C-1%2C5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's multiply the matrices B and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5ET ALIGN=MIDDLE  ALT=\"C%5ET\"   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 3 matrix, this means that the resulting matrix will be a 2 by  3 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%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2Cx%2Cx%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%281%29%2C3%2C2%29%29%28matrix%282%2C3%2Chighlight%281%29%2C3%2C-2%2Chighlight%284%29%2C-1%2C5%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%281%29%2B%281%29%2A%284%29=2%2B4=6 ALIGN=MIDDLE  ALT=\"%282%29%2A%281%29%2B%281%29%2A%284%29=2%2B4=6\"   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=6 ALIGN=MIDDLE  ALT=\"6\"   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%281%29%2C3%2C2%29%29%28matrix%282%2C3%2C1%2Chighlight%283%29%2C-2%2C4%2Chighlight%28-1%29%2C5%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%281%29%2A%28-1%29=6%2B-1=5 ALIGN=MIDDLE  ALT=\"%282%29%2A%283%29%2B%281%29%2A%28-1%29=6%2B-1=5\"   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=5 ALIGN=MIDDLE  ALT=\"5\"   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 3rd column of the second matrix. After multiplying, add the values:\r<BR>\n" );
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document.write( "1st row, 3rd column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%281%29%2C3%2C2%29%29%28matrix%282%2C3%2C1%2C3%2Chighlight%28-2%29%2C4%2C-1%2Chighlight%285%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " So the element in the 1st row, 3rd column of the resulting matrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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%282%2C2%2C6%2C5%2C1%2Cx%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C6%2C5%2C1%2Cx%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
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document.write( "\n" );
document.write( "================================================================================\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%2C1%2Chighlight%283%29%2Chighlight%282%29%29%29%28matrix%282%2C3%2Chighlight%281%29%2C3%2C-2%2Chighlight%284%29%2C-1%2C5%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=%283%29%2A%281%29%2B%282%29%2A%284%29=3%2B8=11 ALIGN=MIDDLE  ALT=\"%283%29%2A%281%29%2B%282%29%2A%284%29=3%2B8=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
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=11 ALIGN=MIDDLE  ALT=\"11\"   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%282%2C2%2C6%2C5%2C1%2C11%2Cx%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C6%2C5%2C1%2C11%2Cx%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------------------------------\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" );
document.write( "\n" );
document.write( "2nd row, 2nd column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C1%2Chighlight%283%29%2Chighlight%282%29%29%29%28matrix%282%2C3%2C1%2Chighlight%283%29%2C-2%2C4%2Chighlight%28-1%29%2C5%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=%283%29%2A%283%29%2B%282%29%2A%28-1%29=9%2B-2=7 ALIGN=MIDDLE  ALT=\"%283%29%2A%283%29%2B%282%29%2A%28-1%29=9%2B-2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
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=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( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C6%2C5%2C1%2C11%2C7%2Cx%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C6%2C5%2C1%2C11%2C7%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------------------------------\r<BR>\n" );
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document.write( "Multiply the corresponding entries from the 2nd row of the first matrix by the 3rd column of the second matrix. After multiplying, add the values:\r<BR>\n" );
document.write( "\n" );
document.write( "2nd row, 3rd column: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C1%2Chighlight%283%29%2Chighlight%282%29%29%29%28matrix%282%2C3%2C1%2C3%2Chighlight%28-2%29%2C4%2C-1%2Chighlight%285%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=%283%29%2A%28-2%29%2B%282%29%2A%285%29=-6%2B10=4 ALIGN=MIDDLE  ALT=\"%283%29%2A%28-2%29%2B%282%29%2A%285%29=-6%2B10=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<BR>\n" );
document.write( "\n" );
document.write( " So the element in the 2nd row, 3rd 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" );
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%282%2C2%2C6%2C5%2C1%2C11%2C7%2C4%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C2%2C6%2C5%2C1%2C11%2C7%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------------------------------\r<BR>\n" );
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document.write( "<BR>\n" );
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document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==============================================================================\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%2C3%2C6%2C5%2C1%2C11%2C7%2C4%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C3%2C6%2C5%2C1%2C11%2C7%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5ET=%28matrix%282%2C2%2C2%2C1%2C3%2C2%29%29%2A%28matrix%282%2C2%2C1%2C3%2C-2%2C4%2C-1%2C5%29%29=%28matrix%282%2C3%2C6%2C5%2C1%2C11%2C7%2C4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which in short means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5ET=%28matrix%282%2C3%2C6%2C5%2C1%2C11%2C7%2C4%29%29 ALIGN=MIDDLE  ALT=\"BC%5ET=%28matrix%282%2C3%2C6%2C5%2C1%2C11%2C7%2C4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );