Rather than assess whether my students can do matrix multiplication by having them multiply matrices without a calculator, I decided to ask a different question. After all, the point is about understanding and not computation, right? So, instead of giving them a non-calculator section on their quiz, I changed the question:
Given that
![\left[ \begin{array} {cc} 5 & 2\\ 7 & 3\end{array} \right] \left[ \begin{array} {cc} 1 & -4\\ -6 & 9\end{array} \right]= \left[ \begin{array} {cc} -7 & -2\\ -11 & -1\end{array} \right]](https://s0.wp.com/latex.php?latex=%5Cleft%5B++%5Cbegin%7Barray%7D+%7Bcc%7D++5+%26+2%5C%5C++7+%26+3%5Cend%7Barray%7D++%5Cright%5D++%5Cleft%5B++%5Cbegin%7Barray%7D+%7Bcc%7D++1+%26+-4%5C%5C++-6+%26+9%5Cend%7Barray%7D++%5Cright%5D%3D++%5Cleft%5B++%5Cbegin%7Barray%7D+%7Bcc%7D++-7+%26+-2%5C%5C++-11+%26+-1%5Cend%7Barray%7D++%5Cright%5D++&bg=ffffff&fg=333333&s=0&c=20201002)
explain the calculation that gives the entry in the first row, second column of the product matrix.
rawsonmath 