Exam 7: Matrix Algebra

Use the matrix operations on a graphing calculator to find her income if increasing it two times would cause her profit to be three times as large.(Round to the nearest thousand dollars.)

Solve by the method of reduction:

Find the income earned by the nuclear industry and its cost for the other forms of energy it uses.Then calculate its profit.

For one animal,she determines that she needs to combine these bags to get 15,000 g of ,30,000 g of ,and 19,000 g of )How many bags of each type of food should she order?

A bookstore has 100 dictionaries,70 cookbooks,and 90 thesauruses in stock,and a second store with 85 dictionaries,95 cookbooks,and 60 thesauruses in stock.If the value of each dictionary is $28,each cookbook is $22 and each thesaurus is $16,use the matrix operations on a graphing calculator to find the total value of the bookstore's inventory.

The researcher then changes the original demand matrix using the matrix equation = A + 0.2D,where A = .Use the matrix operations on a graphing calculator to calculate the new demand matrix in his model.

If the letters to be encoded are L = ,show that E(FL)= (EF)L.

Suppose that a simple economy consists of three sectors: agriculture (A),manufacturing (M),and transportation (T).Economists have determined that to produce one unit of A requires units of A, units of B,and units of T,while production of one unit of M requires units of A, units of M,and units of T,and production of one unit of T requires units of A, units of M,and units of T.There is an external demand for 20 units of A,40 units of M,and 10 units of T.Determine the production levels necessary to meet the external demand.

Solve by the method of reduction:

A pet store has 6 kittens,10 puppies,and 7 parrots in stock,and a second store with 8 kittens,14 puppies,and 9 parrots in stock.If the value of each kitten is $55,each puppy is $150 and each parrot is $35,find the total value of the pet store's inventory.

Use the encoding matrix , an additional coding matrix, plus the matrices and to answer the question. -

Set up a matrix equation with integer values that is equivalent to the system of equations. -

Give an example of 2 matrices A and B where A × B ≠ B × A.

Solve by the method of reduction:

By using matrix reduction,solve the system:

Find all solutions by reducing the matrix:

A client wants 26 blocks of high-risk stock,25 blocks of moderate-risk stock,and 29 blocks of low-risk stock.Use the matrix operations on a graphing calculator to find how many of each portfolio should be suggested.

If A = and B = ,find BA.

Solve the following system of equations by reducing the matrix:

What is the change in sales between 1994 and 1995?