input-output matrix for prod. processess of three industries

[Navyguy]

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

A = 0.10  0.15  0.10
    0.20  0.05  0.08
    0.04  0.06  0.02

X = 500  800  400

My answer is 210, 172, 76 but I'm not sure. Thanks for any help given.

 

[pka]

Frankly the answer depends on the way the matrices are written!
For your answer to be correct the X matrix would be a column matrix.
But you have written as a row matrix.
\(\displaystyle \left[ {\begin{array}{ccc}
{{\rm{0}}{\rm{.1}}} & {{\rm{0}}{\rm{.15}}} & {{\rm{0}}{\rm{.1}}} \\
{{\rm{0}}{\rm{.2}}} & {{\rm{0}}{\rm{.05}}} & {{\rm{0}}{\rm{.08}}} \\
{{\rm{0}}{\rm{.04}}} & {{\rm{0}}{\rm{.06}}} & {{\rm{0}}{\rm{.02}}} \\
\end{array}} \right]\left[ {\begin{array}{c}
{500} \\
{800} \\
{400} \\
\end{array}} \right] = \left[ {\begin{array}{c}
{210} \\
{172} \\
{76} \\
\end{array}} \right].\)

 

[Navyguy]

thanks

Thanks for checking my answer.