Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final output of each industry so that the demand of both industry and the open sector are met.

Solve the matrix equation given that

  and  . 

Jackson Farms have alloted a certain amount of land for cultivating soybeans, corn and wheat. Cultivating 1 acre of soybeans requires 3 labor-hours, and cultivating 1 acre of corn or wheat requires 6 labor-hours. The cost of seeds for 1 acre of soybeans is $15, for 1 acre of corn is $23, and for 1 acre of wheat is $14. If all resources are to be used, how many acres of each crop should be cultivated if the following hold?

1,300 acres of land are alloted, 5,700 labor-hours are available and $21,600 is available for seeds.  

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Find the inverse of the given matrix, if it exists. Verify your answer.

Let and

Find , and

Write a matrix equation that is equivalent to the system of linear equations and solve the system.