1. **State the problem:** We have a transaction matrix representing the purchases between sectors X, Y, and Z. We need to find the input-output matrix and then calculate the gross output for an anticipated demand of 300, 1000, and 900 units respectively for the sectors. 2. **Given data:** Transaction matrix (each element $a_{ij}$ represents purchases of sector i from sector j): $$A = \begin{bmatrix}300 & 400 & 350\\ ? & ? & ? \\ ? & ? & ? \end{bmatrix}$$ Note: The matrix is incomplete from the input. Assuming the question meant the transaction matrix is fully provided or that missing data corresponds to zero or unknown. To continue, assume the purchase matrix $A$ as: $$A = \begin{bmatrix}300 & 400 & 350\\ a & b & c \\ d & e & f \end{bmatrix}$$ 3. **Compute total output for each sector:** Sum of the columns gives total output $x_j$ for sector $j$. But without complete matrix, let's define total output vector $x = [x_X, x_Y, x_Z]^T$. 4. **Input-output coefficients matrix $B$: ** Coefficients are obtained by dividing each element of $A$ by the total output of the sector it was purchased from: $$b_{ij} = \frac{a_{ij}}{x_j}$$ 5. **Equation for gross output:** $$x = Bx + d$$ where $d$ = final demand vector = $[300, 1000, 900]^T$. Solving for $x$: $$x - Bx = d \\ (I - B)x = d \\ x = (I - B)^{-1} d$$ 6. **Calculate $B$ from $A$ and $x$, then compute $x$.** Since $A$ and $x$ are not fully given, assume example values or prompt user for full transaction matrix to proceed. In summary: - Obtain total output $x_j$ by summing columns of $A$. - Calculate input-output matrix $B$ via $b_{ij} = \frac{a_{ij}}{x_j}$. - Calculate gross output $x = (I-B)^{-1} d$ where $d= [300,1000,900]^T$. **Final Answer:** Gross outputs $x$ calculated from above once complete matrix is known.