Exam 7: Matrix Algebra

A manufacturer who produces products A,B,and C is only interested in tracking labor costs.What is the order of the matrix he would use?

Perform the indicated operations and simplify your answer: 2 -

Use the matrix operations on a graphing calculator to find the transpose of

Use the encoding matrix an additional coding 1 matricx plus the matrices to answer the question. -EO

The spa staff determines that a client should take 190% of the RDA of vitamin A,150% of the RDA of vitamin C,and 120% of the RDA of vitamin D each day.How many tablets of each supplement should he take each day?

Solve by the method of reduction:

Find a 3 × 2 matrix with = = 0,all other equal to 1.

On Sundays and holidays,the company must move 14 tons of mail,9 tons of medical supplies,and 11 tons of freight.This system of equations can be represented by the matrix: .Reduce this matrix to calculate how many aircraft of each type should be used.

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

A client wants 33 blocks of high-risk stock,27 blocks of moderate-risk stock,and 30 blocks of low-risk stock.How many of each portfolio should be suggested.

What is the change in sales between 1994 and 1996?

The prices (in dollars per case)for 3 types of pens are represented by the price vector: P = .An office supply store orders cases of these pens in the quantities given by the column vector: Q = .Find the total cost (in dollars)of the purchase.

A new EPA mandate requires that all energy users reduce their energy use from the original level by over the next 10 years to minimize global warming.Use the matrix operations on a graphing calculator to calculate a new demand matrix which reflects this decrease.

The price charged for cases of 2 different soft drinks at two different stores can be represented by the matrix The number of cases of each soft drink 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, .

A group of investors has $500,000 to invest in the stocks of three companies.Company A sells for $50 a share and has an expected growth of 13% per year.Company B sells for $20 per share and has an expected growth of 15% per year.Company C sells for $80 a share and has an expected growth of 10% per year.The group decides to try a new investment strategy which entails buying equal amounts of shares in Company B and Company C,and having a goal of 11.4% growth per year.How many shares of each stock should they buy?

If A = ,determine (a) ,and (b)the order of A.

A manufacturer of blended juices will also bottle pure juices for one supermarket chain.This week he bottles cherry,grape,and cranberry juice.Fill in the matrix for the gallons of each juice needed to produce 1 gallon of juice for each of the 3 pure juices.

Find the inverse matrix of .

(Use the matrix operations on a graphing calculator.)

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