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The image contains a Leontief inverse matrix and a demand vector in a three-sector economy. Here's the breakdown of the problem:

The Leontief inverse matrix for the three-sector economy is given as:

\[
\begin{pmatrix}
1.70 & 0.25 & 0.33 \\
0.72 & 1.47 & 0.52 \\
1.18 & 0.59 & 1.76
\end{pmatrix}
\]

The demand vector is provided as:

\[
\text{D} = \begin{pmatrix} 300 \\ 300 \\ 200 \end{pmatrix}
\]

We are asked to find how much total sectoral output is required to meet this level of final demand. 

### Solution Approach:

The total output vector, \(\text{X}\), can be calculated using the equation:

\[
\text{X} = \text{Leontief Inverse} \times \text{D}
\]

Let's multiply the Leontief inverse matrix with the demand vector:

\[
\begin{pmatrix}
1.70 & 0.25 & 0.33 \\
0.72 & 1.47 & 0.52 \\
1.18 & 0.59 & 1.76
\end{pmatrix}
\times
\begin{pmatrix}
300 \\
300 \\
200
\end{pmatrix}
\]

#### Step-by-step multiplication:

1. For the first component of output (\(X_1\)):
\[
X_1 = (1.70 \times 300) + (0.25 \times 300) + (0.33 \times 200) = 510 + 75 + 66 = 651
\]

2. For the second component of output (\(X_2\)):
\[
X_2 = (0.72 \times 300) + (1.47 \times 300) + (0.52 \times 200) = 216 + 441 + 104 = 761
\]

3. For the third component of output (\(X_3\)):
\[
X_3 = (1.18 \times 300) + (0.59 \times 300) + (1.76 \times 200) = 354 + 177 + 352 = 883
\]

Thus, the total sectoral output required is:

\[
\text{X} = \begin{pmatrix} 651 \\ 761 \\ 883 \end{pmatrix}
\]

### Final Answer:
The total sectoral output needed to realize the final demand of \(D_1 = 300\), \(D_2 = 300\), and \(D_3 = 200\) is:
\[
X_1 = 651, \quad X_2 = 761, \quad X_3 = 883
\]

Would you like more details on any part of the process, or do you have other questions?

### Follow-up Questions:
1. How does the Leontief inverse matrix affect the overall output in an economy?
2. What happens to the total output if the final demand increases uniformly across all sectors?
3. Can you explain the concept of input-output analysis in relation to the Leontief inverse?
4. What are the economic implications of having larger values in the Leontief inverse matrix?
5. How can changes in one sector's demand affect the other sectors in this model?

#### Tip:
When working with economic models like the Leontief model, always ensure that the matrix is non-singular to guarantee that the inverse exists, which is critical for meaningful economic interpretations.

The Leontief inverse of a three-sector economy is given by a matrix. The government has planned a final demand of 800, with sectoral components being D1=300, D2=300, D3=200. How much total sectoral output will be required to realize this level of final demand?

Learn how to calculate the total sectoral output required to meet a final demand using the Leontief inverse matrix. The problem involves matrix multiplication and input-output analysis for a three-sector economy, with a final demand of D1=300, D2=300, and D3=200.

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