If the matrix of technical coefficients is A = bmatrix 0.1 & 0.2 \\ 0.3 & 0.4 bmatrix then Leontief matrix is a) bmatrix 0.1 & 0.2 \\ 0.3 & 0.4 bmatrix b) bmatrix 0.9 & 0.2 \\ 0.3 & 0.6 bmatrix c)…

The Leontief inverse matrix (also called the open matrix) is derived by subtracting the technical coefficients matrix $A$ from the identity matrix $I$. The formula is:

$$I-A$$

Given: $$A=\left[\begin{array}{cc}0.1& 0.2\\ 0.3& 0.4\end{array}\right],I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$

Compute $I-A$:

$$I-A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}0.1& 0.2\\ 0.3& 0.4\end{array}\right]=\left[\begin{array}{cc}1-0.1& 0-0.2\\ 0-0.3& 1-0.4\end{array}\right]=\left[\begin{array}{cc}0.9& -0.2\\ -0.3& 0.6\end{array}\right]$$

Thus, the correct Leontief matrix is:

$$\boxed{\left[\begin{array}{cc}0.9& -0.2\\ -0.3& 0.6\end{array}\right]}$$

Answer: c) $\left[\begin{array}{cc}0.9& -0.2\\ -0.3& 0.6\end{array}\right]$