Rodriquez Henry
06/18/2024 · Elementary School
S \( =\left[\begin{array}{rr}2 & 6 \\ 8 & 12 \\ 7 & 3\end{array}\right] \) (Type an integer or decimal for each matrix element.) b) Write a row matrix C that represents the cost, per dozen, of the ingredients for each type of cookie. Maintain the ordering of cookie types from the table. \( \mathrm{C}=\left[\begin{array}{lll}3.50 & 2.50 & 1.50\end{array}\right] \) (Type an integer or decimal for each matrix element.) c) Find the product CS. CS = \( \square \) (Type an integer or decimal for each matrix element.)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the product \( CS \), we need to multiply the row matrix \( C \) by the matrix \( S \).
Given:
\[
S = \begin{bmatrix}
2 & 6 \\
8 & 12 \\
7 & 3
\end{bmatrix}
\]
and
\[
C = \begin{bmatrix}
3.50 & 2.50 & 1.50
\end{bmatrix}
\]
The product \( CS \) is calculated as follows:
\[
CS = C \cdot S = \begin{bmatrix}
3.50 & 2.50 & 1.50
\end{bmatrix} \cdot \begin{bmatrix}
2 & 6 \\
8 & 12 \\
7 & 3
\end{bmatrix}
\]
To perform the multiplication, we calculate each element of the resulting matrix:
1. First element:
\[
(3.50 \cdot 2) + (2.50 \cdot 8) + (1.50 \cdot 7) = 7.00 + 20.00 + 10.50 = 37.50
\]
2. Second element:
\[
(3.50 \cdot 6) + (2.50 \cdot 12) + (1.50 \cdot 3) = 21.00 + 30.00 + 4.50 = 55.50
\]
Thus, the product \( CS \) is:
\[
CS = \begin{bmatrix}
37.50 & 55.50
\end{bmatrix}
\]
So, the final answer is:
\[
CS = \begin{bmatrix}
37.50 & 55.50
\end{bmatrix}
\]
Quick Answer
CS = \( \begin{bmatrix}
37.50 & 55.50
\end{bmatrix} \)
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