<PRE><B>Question 636414</B>
Since the first matrix is a &lt;font color=&quot;red&quot;&gt;2&lt;/font&gt; by 2 matrix and the second matrix is a 2 by &lt;font color=&quot;green&quot;&gt;2&lt;/font&gt; matrix, this means that the resulting matrix will be a &lt;font color=&quot;red&quot;&gt;2&lt;/font&gt; by &lt;font color=&quot;green&quot;&gt;2&lt;/font&gt; 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.&lt;br&gt;

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  So the final resulting matrix will look like:&lt;br&gt;
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  &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Cx%2Cx%2Cx%2Cx%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2Cx%2Cx%2Cx%2Cx%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;
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  note: the &quot;x&quot;s are just placeholders for now&lt;br&gt;
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  &lt;br&gt;&lt;br&gt;--------------------------------------------------&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Multiply the corresponding entries from the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;1st&lt;/font&gt; row of the first matrix by the &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;1st&lt;/font&gt; column of the second matrix. After multiplying, add the values:&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;1st&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;1st&lt;/font&gt; column: &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%283%29%2C1%2C4%29%29%28matrix%282%2C2%2Chighlight%280%29%2C-2%2Chighlight%281%29%2C5%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%283%29%2C1%2C4%29%29%28matrix%282%2C2%2Chighlight%280%29%2C-2%2Chighlight%281%29%2C5%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%282%29%2A%280%29%2B%283%29%2A%281%29=0%2B3=3&amp;amp;x=0003&quot; alt=&quot;%282%29%2A%280%29%2B%283%29%2A%281%29=0%2B3=3&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt; So the element in the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;1st&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;1st&lt;/font&gt; column of the resulting matrix is &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=3&amp;amp;x=0003&quot; alt=&quot;3&quot; align=&quot;MIDDLE&quot;&gt;. Now let&#39;s update the matrix:&lt;br&gt;&lt;br&gt; &lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2Cx%2Cx%2Cx%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C3%2Cx%2Cx%2Cx%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;--------------------------------------------------&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Multiply the corresponding entries from the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;1st&lt;/font&gt; row of the first matrix by the &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;2nd&lt;/font&gt; column of the second matrix. After multiplying, add the values:&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;1st&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;2nd&lt;/font&gt; column: &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%283%29%2C1%2C4%29%29%28matrix%282%2C2%2C0%2Chighlight%28-2%29%2C1%2Chighlight%285%29%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2Chighlight%282%29%2Chighlight%283%29%2C1%2C4%29%29%28matrix%282%2C2%2C0%2Chighlight%28-2%29%2C1%2Chighlight%285%29%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%282%29%2A%28-2%29%2B%283%29%2A%285%29=-4%2B15=11&amp;amp;x=0003&quot; alt=&quot;%282%29%2A%28-2%29%2B%283%29%2A%285%29=-4%2B15=11&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt; So the element in the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;1st&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;2nd&lt;/font&gt; column of the resulting matrix is &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=11&amp;amp;x=0003&quot; alt=&quot;11&quot; align=&quot;MIDDLE&quot;&gt;. Now let&#39;s update the matrix:&lt;br&gt;&lt;br&gt; &lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2C11%2Cx%2Cx%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C3%2C11%2Cx%2Cx%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;================================================================================&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Multiply the corresponding entries from the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;2nd&lt;/font&gt; row of the first matrix by the &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;1st&lt;/font&gt; column of the second matrix. After multiplying, add the values:&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;2nd&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;1st&lt;/font&gt; column: &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C3%2Chighlight%281%29%2Chighlight%284%29%29%29%28matrix%282%2C2%2Chighlight%280%29%2C-2%2Chighlight%281%29%2C5%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C2%2C3%2Chighlight%281%29%2Chighlight%284%29%29%29%28matrix%282%2C2%2Chighlight%280%29%2C-2%2Chighlight%281%29%2C5%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%281%29%2A%280%29%2B%284%29%2A%281%29=0%2B4=4&amp;amp;x=0003&quot; alt=&quot;%281%29%2A%280%29%2B%284%29%2A%281%29=0%2B4=4&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt; So the element in the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;2nd&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;1st&lt;/font&gt; column of the resulting matrix is &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=4&amp;amp;x=0003&quot; alt=&quot;4&quot; align=&quot;MIDDLE&quot;&gt;. Now let&#39;s update the matrix:&lt;br&gt;&lt;br&gt; &lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2C11%2C4%2Cx%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C3%2C11%2C4%2Cx%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;--------------------------------------------------&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Multiply the corresponding entries from the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;2nd&lt;/font&gt; row of the first matrix by the &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;2nd&lt;/font&gt; column of the second matrix. After multiplying, add the values:&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;2nd&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;2nd&lt;/font&gt; column: &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C3%2Chighlight%281%29%2Chighlight%284%29%29%29%28matrix%282%2C2%2C0%2Chighlight%28-2%29%2C1%2Chighlight%285%29%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C2%2C3%2Chighlight%281%29%2Chighlight%284%29%29%29%28matrix%282%2C2%2C0%2Chighlight%28-2%29%2C1%2Chighlight%285%29%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%281%29%2A%28-2%29%2B%284%29%2A%285%29=-2%2B20=18&amp;amp;x=0003&quot; alt=&quot;%281%29%2A%28-2%29%2B%284%29%2A%285%29=-2%2B20=18&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt; So the element in the &lt;font size=&quot;4&quot; color=&quot;red&quot;&gt;2nd&lt;/font&gt; row, &lt;font size=&quot;4&quot; color=&quot;green&quot;&gt;2nd&lt;/font&gt; column of the resulting matrix is &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=18&amp;amp;x=0003&quot; alt=&quot;18&quot; align=&quot;MIDDLE&quot;&gt;. Now let&#39;s update the matrix:&lt;br&gt;&lt;br&gt; &lt;br&gt;&lt;br&gt;&lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;==============================================================================&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Answer:&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;So the solution is  &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;

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  In other words,&lt;br&gt;
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  &lt;img src=&quot;/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C2%2C2%2C3%2C1%2C4%29%29%2A%28matrix%282%2C2%2C0%2C-2%2C1%2C5%29%29=%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29&amp;amp;x=0003&quot; alt=&quot;%28matrix%282%2C2%2C2%2C3%2C1%2C4%29%29%2A%28matrix%282%2C2%2C0%2C-2%2C1%2C5%29%29=%28matrix%282%2C2%2C3%2C11%2C4%2C18%29%29&quot; align=&quot;MIDDLE&quot;&gt;&lt;br&gt;
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