document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=441330>Question 441330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> compute the matrix product AB for:<BR>\n" );
document.write( " A = <BR>\n" );
document.write( "     [2  3  0<BR>\n" );
document.write( "     -4  2  1<BR>\n" );
document.write( "      3  0 -2]<BR>\n" );
document.write( "    <BR>\n" );
document.write( "B = <BR>\n" );
document.write( "    [-1  2  3<BR>\n" );
document.write( "     3  0 -2<BR>\n" );
document.write( "     0  4  0]<BR>\n" );
document.write( "                                  <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 #837478 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=837478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I don't recommend using and/or memorizing the formula the tutor Edwin mentioned.\r<BR>\n" );
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document.write( "Instead it is better to highlight the first row of matrix A and first column of matrix B.\r<BR>\n" );
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document.write( "We'll align the terms like so<BR>\n" );
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document.write( "<tr><TD >row1 of A:</TD><TD >2</TD><TD >3</TD><TD >0</TD></tr><tr><TD >column1 of B:</TD><TD >-1</TD><TD >3</TD><TD >0</TD></tr>\n" );
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document.write( "Multiply straight down (eg: 2*(-1) = -2)<BR>\n" );
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document.write( "<tr><TD >row1 of A:</TD><TD >2</TD><TD >3</TD><TD >0</TD></tr><tr><TD >column1 of B:</TD><TD >-1</TD><TD >3</TD><TD >0</TD></tr><tr><TD >Product:</TD><TD >-2</TD><TD >9</TD><TD >0</TD></tr>\n" );
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document.write( "Then add up the products to get -2+9+0 = 7\r<BR>\n" );
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document.write( "This result of 7 is the entry in the answer matrix that is in the first row and first column.\r<BR>\n" );
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document.write( "The answer is of the format <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C7%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C7%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Follow this thought process for the other entries.\r<BR>\n" );
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document.write( "For instance, the 2nd row and 3rd column of the answer will involve row2 of A and column3 of B.<BR>\n" );
document.write( "Let me know if you have further questions.\r<BR>\n" );
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document.write( "Here's a similar example<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"400px\" src = \"https://miro.medium.com/v2/resize:fit:1100/format:webp/1*YGcMQSr0ge_DGn96WnEkZw.png\"><BR>\n" );
document.write( "Image Source:<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://towardsdatascience.com/a-complete-beginners-guide-to-matrix-multiplication-for-data-science-with-python-numpy-9274ecfc1dc6\">https://towardsdatascience.com/a-complete-beginners-guide-to-matrix-multiplication-for-data-science-with-python-numpy-9274ecfc1dc6</a>\r<BR>\n" );
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document.write( "Another example<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://www.mathsisfun.com/algebra/images/matrix-multiply-b.svg\"><BR>\n" );
document.write( "Image Source<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/algebra/matrix-multiplying.html\">https://www.mathsisfun.com/algebra/matrix-multiplying.html</a><BR>\n" );
document.write( "The scratch work highlighted in yellow would be something like this<BR>\n" );
document.write( "1*8 + 2*10 + 3*12 = 8 + 20 + 36 = 64<BR>\n" );
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