Model II II IV CA 21 16 13 11 A = AR 15 12 6. 4 NV 14 17 10 8 e estimated profits (in thousands of dollars) for each model in California, Arizona, and Nevada are represented by the matrices B, C, and D, respectively. 1 [60 I [45] 1 [40 II B = 70 C = II 55 D III| 70 II 45 III 90 III| 60 IV [120 IV [90 IV [80 ) Let E = 100 and find (EA)B. --EEE 21 16 13 11 (EA)B = 15 12 6 4 14 17 10 aF-[010]a ) Let F =01o and find (FA)C. 21 16 13 11 (FA)C = 15 12 6 4 14 17 10 8
Model II II IV CA 21 16 13 11 A = AR 15 12 6. 4 NV 14 17 10 8 e estimated profits (in thousands of dollars) for each model in California, Arizona, and Nevada are represented by the matrices B, C, and D, respectively. 1 [60 I [45] 1 [40 II B = 70 C = II 55 D III| 70 II 45 III 90 III| 60 IV [120 IV [90 IV [80 ) Let E = 100 and find (EA)B. --EEE 21 16 13 11 (EA)B = 15 12 6 4 14 17 10 aF-[010]a ) Let F =01o and find (FA)C. 21 16 13 11 (FA)C = 15 12 6 4 14 17 10 8
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Matrix Application in Real Estate Development: Bond Brothers**
Bond Brothers, a real estate developer, builds single-family houses in California, Arizona, and Nevada. The proposed number of units (in hundreds) of each model to be built in each state is given by the matrix \( A \):
\[
A = \begin{bmatrix}
21 & 16 & 13 & 11 \\
15 & 12 & 6 & 4 \\
14 & 17 & 10 & 8
\end{bmatrix}
\]
Where:
- Rows represent states: CA (California), AR (Arizona), NV (Nevada).
- Columns represent models: I, II, III, IV.
The estimated profits (in thousands of dollars) for each model in California, Arizona, and Nevada are represented by the matrices \( B \), \( C \), and \( D \), respectively:
\[
B = \begin{bmatrix}
60 \\
70 \\
90 \\
120
\end{bmatrix}
\quad
C = \begin{bmatrix}
45 \\
55 \\
70 \\
90
\end{bmatrix}
\quad
D = \begin{bmatrix}
40 \\
45 \\
60 \\
80
\end{bmatrix}
\]
### Exercise
**(a)** Let \( E = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix} \) and find \( (EA)B \).
\[
E = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix}
\]
\[
(EA) = \begin{bmatrix}
21 & 16 & 13 & 11
\end{bmatrix}
\]
\[
(EA)B = \begin{bmatrix}
21 & 16 & 13 & 11
\end{bmatrix}
\begin{bmatrix}
60 \\
70 \\
90 \\
120
\end{bmatrix}
\]
Multiplying the vectors:
\[
(21 \cdot 60) + (16 \cdot 70) + (13 \cdot 90) + (11 \cdot 120)
\]
Therefore, the calculation proceeds as follows:
\[
1260 + 1120 + 1170 + 1320 = 4870
\]
Thus, \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c4f1739-57e2-4399-a976-93f96ef5c2b4%2F7e3bb18f-a40b-4a3a-95c9-d0fe6168a6af%2Fealud2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Application in Real Estate Development: Bond Brothers**
Bond Brothers, a real estate developer, builds single-family houses in California, Arizona, and Nevada. The proposed number of units (in hundreds) of each model to be built in each state is given by the matrix \( A \):
\[
A = \begin{bmatrix}
21 & 16 & 13 & 11 \\
15 & 12 & 6 & 4 \\
14 & 17 & 10 & 8
\end{bmatrix}
\]
Where:
- Rows represent states: CA (California), AR (Arizona), NV (Nevada).
- Columns represent models: I, II, III, IV.
The estimated profits (in thousands of dollars) for each model in California, Arizona, and Nevada are represented by the matrices \( B \), \( C \), and \( D \), respectively:
\[
B = \begin{bmatrix}
60 \\
70 \\
90 \\
120
\end{bmatrix}
\quad
C = \begin{bmatrix}
45 \\
55 \\
70 \\
90
\end{bmatrix}
\quad
D = \begin{bmatrix}
40 \\
45 \\
60 \\
80
\end{bmatrix}
\]
### Exercise
**(a)** Let \( E = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix} \) and find \( (EA)B \).
\[
E = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix}
\]
\[
(EA) = \begin{bmatrix}
21 & 16 & 13 & 11
\end{bmatrix}
\]
\[
(EA)B = \begin{bmatrix}
21 & 16 & 13 & 11
\end{bmatrix}
\begin{bmatrix}
60 \\
70 \\
90 \\
120
\end{bmatrix}
\]
Multiplying the vectors:
\[
(21 \cdot 60) + (16 \cdot 70) + (13 \cdot 90) + (11 \cdot 120)
\]
Therefore, the calculation proceeds as follows:
\[
1260 + 1120 + 1170 + 1320 = 4870
\]
Thus, \(
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