Question

# 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 i

Matrices
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 $$A=\begin{bmatrix}3 & 7 \\2 & 4 \end{bmatrix} \text{ and } B=\begin{bmatrix}-3 & 6 \\4 & -2 \end{bmatrix}$$

2020-12-22

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 $$2 \times 2$$ matrices,
$$A=\begin{bmatrix}a & b \\c & d \end{bmatrix} , B=\begin{bmatrix}p & q \\r & s \end{bmatrix}$$
the first row of the resultant matrix is as below:
=ap+br
Thus, the resultant matrix is as below:
$$AB=\begin{bmatrix}ap+br & aq+bs \\cp+dr & cq+ds \end{bmatrix}$$
Step 2
We have,
$$A=\begin{bmatrix}3 & 7 \\2 & 4 \end{bmatrix},B=\begin{bmatrix}-3 & 6 \\4 & -2 \end{bmatrix}$$
Therefore.
$$AB=\begin{bmatrix}-9+28 & 18-14 \\-6+16 & 12-8 \end{bmatrix}$$
$$=\begin{bmatrix}19 & 4 \\10 & 4 \end{bmatrix}$$