input-output matrix #2: internal consumption amount

[Navyguy]

For the input-output matrix A, and the output matrix X, of the three industries, find the amounts consumed internally by the production process.

A = 0.15  0.25  0.10
    0.05  0.05  0.12
    0.12  0.16  0.08

X = 1000  2000  2500

My answer is 640, 450, 900. I'm not sure of my answer. Thanks for any help given.

 

[steve_b]

For the input-output matrix A, and the output matrix X, of the three industries, find the amounts consumed internally by the production process.

Code:
A = 0.15 0.25 0.10
0.05 0.05 0.12
0.12 0.16 0.08

X = 1000 2000 2500

My answer is 640, 450, 900. I'm not sure of my answer. Thanks for any help given.

----------------------

As I understand this material, you have to multiply matrices:

A * X = C

If A is a 3x3 matrix, then X has to be a 3x1 matrix, which will yield C as a 3x1 matrix.

    [.15   .25   .10]
A = [.05   .05   .12]
    [.12   .16   .08]

    [1000]
X = [2000]
    [2500]

Multiplication A*X gives:

   [900]
C =[450]
   [640]

Steve

 

[pka]

\(\displaystyle \L
{\rm{A = }}\left[ {\begin{array}{rrr}
{{\rm{0}}{\rm{.15}}} & {{\rm{0}}{\rm{.25}}} & {{\rm{0}}{\rm{.10}}} \\
{{\rm{0}}{\rm{.05}}} & {{\rm{0}}{\rm{.05}}} & {{\rm{0}}{\rm{.12}}} \\
{{\rm{0}}{\rm{.12}}} & {{\rm{0}}{\rm{.16}}} & {{\rm{0}}{\rm{.08}}} \\
\end{array}} \right]\quad \& \quad X = \left[ {\begin{array}{c}
{1000} \\
{2000} \\
{2500} \\
\end{array}} \right]\quad \Rightarrow \quad AX = \left[ {\begin{array}{c}
{900} \\
{450} \\
{640} \\
\end{array}} \right]\)

Navyguy you should have get in the habit of writing the X vector as a column vector if we multiply A*X.

In some treatments X is a row vector and we multiply X*A.
In which case we get [550 750 540] as the output.
You need to check you textbook for the method to use.