Question

Solve the following problems by using the inverse of the matrix involved.

(a) An automobile factory produces two models, A and B. Model A requires 1 labor hour to paint and ( {1}{2} ) labor hour?

Answer 1

To solve the problems using the inverse of a matrix, set up a matrix with the coefficients of the variables involved. Find the inverse of the matrix and multiply it with the given production requirements to solve for the variables.

Step-by-step explanation:

To solve the problems using the inverse of a matrix, we need to set up a matrix with the coefficients of the variables involved in the problem. In this case, the problem involves the production of two car models, A and B, where Model A requires 1 labor hour to paint and Model B requires 1/2 labor hour to paint. We can represent this information as a matrix:

| 1 1/2 |

Next, we can find the inverse of this matrix and multiply it with the given production requirements to solve for the variables. The inverse of the given matrix is:

| 2 -4 |

| -1 2 |

By multiplying the inverse matrix with the production requirements, we get:

| 2 -4 |

| -1 2 |

| 1 | = | 10 |

| m | | 35 |

So, the solution is m = 35. Therefore, Model A needs to produce 35 units to meet the labor requirements.