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
ANSWERED
asked 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 \(A=\begin{bmatrix}3 & 7 \\2 & 4 \end{bmatrix} \text{ and } B=\begin{bmatrix}-3 & 6 \\4 & -2 \end{bmatrix}\)

Answers (1)

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.
\(AB=\begin{bmatrix}-9+28 & 18-14 \\-6+16 & 12-8 \end{bmatrix}\)
\(=\begin{bmatrix}19 & 4 \\10 & 4 \end{bmatrix}\)

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