---## Lesson: Building the Technology Matrix from the Input-Output Table### Example 1: Input-Output TableTo convert the provided input-output data into a technology matrix, please examine the table below:| | To A | To B | To C ||----|------|------|------|| **From A** | 0 | 200 | 450 || **From B** | 400 | 300 | 300 || **From C** | 0 | 0 | 600 |**Total Output:**- From Industry A: 1,000- From Industry B: 2,000- From Industry C: 3,000Below the table is an interactive section that provides support features for further assistance:- **Read It:** Links to a detailed explanation of the concept.- **Watch It:** Links to video tutorials for visual learners.- **Talk to a Tutor:** Offers personalized help through tutoring services.### Steps to Obtain the Technology Matrix1. **Identify the Input and Output Data:** - Use the given table that shows the flow of goods and services between industries A, B, and C. 2. **Calculate the Technology Coefficients:** - For each cell in the matrix, divide the input value by the total output of the 'from' industry. - Example: For Industry A supplying B, the technology coefficient is 200/1000 = 0.2.3. **Construct the Technology Matrix:** - Assemble the calculated coefficients into a matrix format.### Example Technology MatrixUsing the above input-output data, the technology matrix (often referred to as the 'A-matrix') can be assembled:\[\begin{bmatrix}\frac{0}{1000} & \frac{200}{1000} & \frac{450}{1000} \\\frac{400}{2000} & \frac{300}{2000} & \frac{300}{2000} \\\frac{0}{3000} & \frac{0}{3000} & \frac{600}{3000}\end{bmatrix} =\begin{bmatrix}0 & 0.2 & 0.45 \\0.2 & 0.15 & 0.15 \\0 & 0

Here the given input out table is given as:

Answered: Obtain the technology matrix from the…

Obtain the technology matrix from the input-output table. То A В C From A 200 450 B 400 300 300 C 600 Total Output | 1,000 2,000 3,000

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

---

## Lesson: Building the Technology Matrix from the Input-Output Table

### Example 1: Input-Output Table

To convert the provided input-output data into a technology matrix, please examine the table below:

| | To A | To B | To C |
|----|------|------|------|
| **From A** | 0 | 200 | 450 |
| **From B** | 400 | 300 | 300 |
| **From C** | 0 | 0 | 600 |

**Total Output:**
- From Industry A: 1,000
- From Industry B: 2,000
- From Industry C: 3,000

Below the table is an interactive section that provides support features for further assistance:
- **Read It:** Links to a detailed explanation of the concept.
- **Watch It:** Links to video tutorials for visual learners.
- **Talk to a Tutor:** Offers personalized help through tutoring services.

### Steps to Obtain the Technology Matrix

1. **Identify the Input and Output Data:**
- Use the given table that shows the flow of goods and services between industries A, B, and C.

2. **Calculate the Technology Coefficients:**
- For each cell in the matrix, divide the input value by the total output of the 'from' industry.
- Example: For Industry A supplying B, the technology coefficient is 200/1000 = 0.2.

3. **Construct the Technology Matrix:**
- Assemble the calculated coefficients into a matrix format.

### Example Technology Matrix
Using the above input-output data, the technology matrix (often referred to as the 'A-matrix') can be assembled:

\[
\begin{bmatrix}
\frac{0}{1000} & \frac{200}{1000} & \frac{450}{1000} \\
\frac{400}{2000} & \frac{300}{2000} & \frac{300}{2000} \\
\frac{0}{3000} & \frac{0}{3000} & \frac{600}{3000}
\end{bmatrix} =
\begin{bmatrix}
0 & 0.2 & 0.45 \\
0.2 & 0.15 & 0.15 \\
0 & 0

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