Exam 7: Matrix Algebra

Solve the matrix equation: 3 - 2 =

(a)If A is the coefficient matrix of the system ,determine . (b)Use to solve the system.

Show that A + O = A.

Use the matrix operations on a graphing calculator to find the total demand for the four types of energy from the manufacturing facility and the university.

Solve the following system of equations by reduction.

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

Let A = .Find .

Solve by the method of reduction:

A small airline has 3 flights,A,B,and C,to each of 3 cities in Colorado.The matrix N represents the number of passengers carried in November,and matrix D represents the number of passengers carried in December.Write a matrix that shows the total number of passengers carried in these two months. N = ; D =

A manufacturer who requires raw materials A,B,C,D,and E is interested in tracking the costs of these materials from 3 different sources.What is the order of the matrix he would use?

Find the transpose of .

Each day of the holiday season,the company must move 75 tons of mail,50 tons of medical supplies,and 55 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.

Perform the indicated operation and simplify your answer:

Given the coefficient matrix A and the final demand matrix D stated below,find and find the output matrix X. A = C =

A blended juice product requires 5 gallons of apple juice,no orange juice,and 2 gallons of cranberry juice.Construct an ingredient matrix for this product.

Perform the indicated operation and simplify your answer:

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

A researcher is studying the effects on the local economy of changes in the original demand matrix.He models one change by the matrix equation = D + 0.5D.Calculate the new demand matrix in his model.

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

The prices (in dollars per case)for 3 types of frozen pizzas are represented by the price vector: A grocery store orders cases of these pizzas in the quantities given by the column vector: Use the matrix operations on a graphing calculator to find the total cost (in dollars)of the purchase.