Exam 4: Systems of Linear Equations; Matrices

A chain of amusement parks pays experienced workers $240 per week and inexperienced workers $220 per week. The total number of workers and total weekly wages at three different parks are given in the table. How many experienced workers does each park employ? Set up a system of linear equations and solve using matrix inverse methods.

Perform the operation, if possible: -

Solve the linear system corresponding to the following augmented matrix:

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM: -Hurst's Feed & Seed sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $31.00. To another customer he sold 2 bushels of wheat, 3 of corn, and 5 of rye, for $27.60. To a third customer he sold 3 bushels of wheat, 5 of corn, and 2 of rye for $32.70. What was the price per bushel for each of the different grains?Let x represent the price per bushel for wheat, y the price per bushel for corn, and z the price per bushel for rye.

Solve the linear system corresponding to the following augmented matrix:

A textbook economy has only two industries, the electric company and the gas company. Each dollar's worth of the electric company's output requires 0.20 of its own output and 0.4 of the gas company's output. Each dollar's worth of the gas company's output requires 0.50 of its own output and 0.7 of the electric company's output. What should the production of electricity and gas be (in dollars) if there is a $16 M demand for electricity and a $7 M demand for gas?

Two sectors of a textbook economy are (1) communication equipment and (2) components and accessories. In 2005 the input-output table involving these two sectors was as follows. Determine the production levels necessary in these two sectors to meet a demand for $80,000 of equipment and $90,000 of components. Round to significant digits.

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed: -Solve for A: AY - A = B

User row operations to change the matrix to reduced form: -

Which of the following matrices has an inverse?

Find the values of a, b, c, and d that make the matrix equation true. -

Perform the operation, if possible: -

Identify the row operation that produces the resulting matrix: -

Solve the system of equations by elimination: -

The following message was encoded with matrix . Decode this message. 28 64 32 91 30 65 24 60 38 99 42 99 35 82 36 81 46 119 13 31 23 51

Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations: -

Write the system as a matrix equation of the form AX = B: -

Write the matrix equation as a system of linear equations without matrices: -

Determine whether B is the inverse of A: -