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).
$\begin{matrix} A = [\begin{array}{ll} 0.4 & 0.2 \\ 0.3 & 0.1 \end{array}] and D = [\begin{array}{l} 14 \\ 16 \end{array}] . \\ X = [ \end{matrix}$

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$X = [\begin{matrix} 32.917 \\ 28.75 \end{matrix}]$ is the solution to the matrix equation

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

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 $[\begin{matrix} 0.6 & - 0.2 \\ - 0.3 & 0.9 \end{matrix}]$

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

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

Step 6 ： $X = [\begin{matrix} 32.917 \\ 28.75 \end{matrix}]$ is the solution to the matrix equation

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).A=[0.40.20.30.1] and D=[1416].X=[

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