Exam 7: Matrix Algebra

Use the matrix operations on a graphing calculator to find the income earned by the hydroelectric industry and its cost for the other forms of energy it uses.Then calculate its profit.

Using the method of reduction,solve the system:

Three components A,B,and C,are used in the manufacturing of a product.For a production run,100,150,and 200 units of A,B,and C are $2,$1,and $3,respectively.Represent the total cost of A,B,and C by a matrix product.

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

2 - =

An employer offers medical,dental,and life insurance to both salaried and unsalaried employees.She describes her annual costs for these benefits in a matrix,and finds that,after employee contributions,only medical insurance requires an employer contribution of $20,000 for salaried and $15,000 for unsalaried employees.Construct a matrix which shows this result.

A courier service has an order to deliver four products to a factory.The table below gives the specifications of the products. A B C D Volume( )5 2 9 17 Weight(lb)20 10 40 70 Value($)300 200 700 1100 If the company's large van can carry 500 cu ft.; 2100 lb,and is insured for $34,000,how many units of each product can be carried? Write the answer in terms of A,B,C,and D.

If = ,then y =

Show that A + B = B + A.

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

Use the matrix operations on a graphing calculator to find the cost of each type of vehicle.

The price charged for 2 different CDs at two different stores can be represented by the matrix The quantities of each CD sold at each store can be represented by the matrix Show that the transpose of the income generated is equal to the product of the transposes of P and Q in reverse order, .

Determine whether the intersection of the planes: has a unique solution or infinitely many solutions; then solve the system.

Reduce the matrix:

If A = ,B = ,and C = ,find 7A + 6B - 3C.

Use the matrix operations on a graphing calculator to find the profit made by the manufacturer on these orders.

Reduce the matrix:

An electronics store has 35 televisions,15 VCRs,and 25 CD players in stock,and a second store with 45 televisions,25 VCRs,and 30 CD players in stock.If the value of each television is $400,each VCR is $200 and each CD player is $150,find the total value of the electronics store's inventory.

Find the transpose of the matrix:

The price charged for 2 different paperback books at two different bookstores can be represented by the matrix P = .The quantities of each book sold at each store can be represented by the matrix Q = .Use the matrix operations on a graphing calculator to show that the transpose of the income generated is equal to the product of the transposes of P and Q in reverse order, .