texelaare

2020-12-21

Enter the expression that would produce the answer (do include the answer) for row 1 column 1 of the multiplied matrix $A\cdot B$:
List the expression in order with the original values using $\cdot$ for multiplication.
then find $A\cdot B$
If

Benedict

Step 1
To multiply matrix A with matrix B, The number of columns of matrix A and the number of rows of matrix B should be equal.
For multiplication of $2×2$ matrices,
$A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right],B=\left[\begin{array}{cc}p& q\\ r& s\end{array}\right]$
the first row of the resultant matrix is as below:
=ap+br
Thus, the resultant matrix is as below:
$AB=\left[\begin{array}{cc}ap+br& aq+bs\\ cp+dr& cq+ds\end{array}\right]$
Step 2
We have,
$A=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right],B=\left[\begin{array}{cc}-3& 6\\ 4& -2\end{array}\right]$
Therefore.
$AB=\left[\begin{array}{cc}-9+28& 18-14\\ -6+16& 12-8\end{array}\right]$
$=\left[\begin{array}{cc}19& 4\\ 10& 4\end{array}\right]$

Jeffrey Jordon