Certainly! To find the total number of dresses of each color and size that Paul has in stock before any sales were made today, we need to sum the existing inventory with the new arrivals for each corresponding size and color.
Here's a step-by-step breakdown of the matrices given:
Existing Inventory Matrix:
[tex]\[
\begin{array}{cccc}
\text{Red} & \text{Blue} & \text{White} & \text{Green} \\
\text{Small} & 3 & 2 & 1 & 2 \\
\text{Medium} & 5 & 4 & 4 & 2 \\
\text{Large} & 4 & 2 & 1 & 2 \\
\end{array}
\][/tex]
New Stock Matrix:
[tex]\[
\begin{array}{cccc}
\text{Red} & \text{Blue} & \text{White} & \text{Green} \\
\text{Small} & 3 & 2 & 1 & 2 \\
\text{Medium} & 5 & 4 & 4 & 2 \\
\text{Large} & 4 & 2 & 1 & 2 \\
\end{array}
\][/tex]
To find the Total Stock Matrix, we simply add the corresponding elements from the two matrices together.
Small Size:
- Red: [tex]\(3 + 3 = 6\)[/tex]
- Blue: [tex]\(2 + 2 = 4\)[/tex]
- White: [tex]\(1 + 1 = 2\)[/tex]
- Green: [tex]\(2 + 2 = 4\)[/tex]
Medium Size:
- Red: [tex]\(5 + 5 = 10\)[/tex]
- Blue: [tex]\(4 + 4 = 8\)[/tex]
- White: [tex]\(4 + 4 = 8\)[/tex]
- Green: [tex]\(2 + 2 = 4\)[/tex]
Large Size:
- Red: [tex]\(4 + 4 = 8\)[/tex]
- Blue: [tex]\(2 + 2 = 4\)[/tex]
- White: [tex]\(1 + 1 = 2\)[/tex]
- Green: [tex]\(2 + 2 = 4\)[/tex]
So, the total stock of dresses for each color and size is:
[tex]\[
\begin{array}{cccc}
\text{Red} & \text{Blue} & \text{White} & \text{Green} \\
\text{Small} & 6 & 4 & 2 & 4 \\
\text{Medium} & 10 & 8 & 8 & 4 \\
\text{Large} & 8 & 4 & 2 & 4 \\
\end{array}
\][/tex]
Hence, this matrix shows the total number of dresses of each color and size that Paul has in stock before any sales were made today:
[tex]\[
\left[\begin{array}{llll}6 & 4 & 2 & 4 \\ 10 & 8 & 8 & 4 \\ 8 & 4 & 2 & 4\end{array}\right]
\][/tex]
