Use the input-output matrix $A$ and the consumer demand matrix $D$ to solve the matrix equation $(I-A) X=D$ for the total output matrix $X$. (Round your answers to three decimal places). \[ \begin{array}{c} A=\left[\begin{array}{ll} 0.4 & 0.2 \\ 0.3 & 0.1 \end{array}\right] \text { and } D=\left[\begin{array}{l} 14 \\ 16 \end{array}\right] . \\ X=[ \end{array} \]

Step 1 ：Given the input-output matrix \(A = \begin{bmatrix} 0.4 & 0.2 \\ 0.3 & 0.1 \end{bmatrix}\) and the consumer demand matrix \(D = \begin{bmatrix} 14 \\ 16 \end{bmatrix}\)

Step 2 ：We need to solve the matrix equation \((I-A)X = D\) for the total output matrix \(X\), where \(I\) is the identity matrix

Step 3 ：First, calculate \(I - A\) to get \(\begin{bmatrix} 0.6 & -0.2 \\ -0.3 & 0.9 \end{bmatrix}\)

Step 4 ：Next, find the inverse of \(I - A\), denoted as \((I - A)^{-1}\), which is \(\begin{bmatrix} 1.875 & 0.41666667 \\ 0.625 & 1.25 \end{bmatrix}\)

Step 5 ：Finally, multiply \((I - A)^{-1}\) with \(D\) to get \(X\), which is \(\begin{bmatrix} 32.917 \\ 28.75 \end{bmatrix}\)

Step 6 ：\(\boxed{X = \begin{bmatrix} 32.917 \\ 28.75 \end{bmatrix}}\) is the solution to the matrix equation