SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 Assn.-.7 Name Perform the operation, if possible. ) Let A = and B = Find AB. ) -6-9 ) Let A = - 5 and B = Find AB. ) ) ) ) If a and b are nonzero real numbers and A = b ab -ab -a, find A. ) 5) A = 0, B = -. Find BA. 5) AB is not defined ) Let B = - -. Find -B. 6)

2 Perform the indicated operations given the matrices. 7) Let C = - and D = - - ; C - D 7) ) Let A = 6 and B = 0-6 ; A + B 8) Solve the problem. 9) A retail company offers, through two different stores in a city, three models, A, B, and C, of a particular brand of camping stove. The inventory of each model on hand in each store is summarized in matrix M. Wholesale (W) and retail (R) prices of each model are summarized in matrix M. Find the product MN and label its columns and rows appropriately. What is the wholesale value of the inventory in Store? A B C W R M = 0 $60 $90 Store N = $0 $50 0 Store $0 $50 A B C 9) 0) Given A = , B = 7 -, C = 9-5, and D = 0, determine which of the following - 6 products is NOT defined. DB AD DA BC 0) Find the inverse, if it exists, of the given matrix. ) Does not exist ) ) Use Gauss-Jordan elimination to find the inverse of. )

3 Determine whether B is the inverse of A ) A = - -, B = Yes No ) ) Use Gauss-Jordan elimination, without introducing fractions, to find the inverse of ) Use the given encoding matrix A to solve the problem. 5) The following message was encoded with matrix. Decode this message. 5) Find the inverse, if it exists, of the given matrix. 6) ) 7) Does not exist 7) Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations. 8) )

4 9) ) Use the given encoding matrix A to solve the problem. 0) A message has been encoded and the matrix which the receiver gets is shown below. 0) The encoding matrix A which was used to encode the message is: A = 0 Find the decoding matrix A-, and use it to decode the message. Assume that the numerical assignment used was a =, b =,..., z = 6, space = 0, period = 0, and apostrophe = 60. EAT YOUR VEGETABLES DRINK ENOUGH COKE DRINK ENOUGH MILK EAT YOUR BROCCOLI Solve the system as matrix equations using inverses. ) -5x + x = 8 x - 6x = -0 (-6, -) (-, -6) (6, ) (, 6) ) There were 0 people at a play. The admission price was $ for adults and $ for children. The admission receipts were $90. How many adults and how many children attended? adults and 8 children 50 adults and 90 children 90 adults and 50 children 95 adults and 5 children ) ) ) Solve the matrix equation 5 matrix. x x + 5 = 8 by using the inverse of the coefficient )

5 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 Y: XY + ZY = A ) Y = X-(A - ZY) Y = (X + Z)- A Y = A(X + Z)- Y = X-(A - Z) The system cannot be solved by matrix inverse methods. Find a method that could be used and then solve the system. 5) -x + 6x = 5) 6x - 8x = x = t + for any real number t, x = 0 x = t + 6, x = t for any real number t No Solution x = t +, x = t for any real number t Solve the problem. 6) Given the technology matrix M and the final demand matrix D stated below, find (I - M)- and find the output matrix X. 6) M = D = ) A large oil company produces three grades of gasoline: regular, unleaded, and super-unleaded. To produce these gasolines, equipment is used which requires as input certain amounts of each of the three grades of gasoline. To produce a dollar's worth of regular requires inputs of $0. worth of regular, $0.8 worth of unleaded, and $0.7 worth of super-unleaded. To produce a dollar's worth of unleaded requires inputs of $0. worth of regular, $0.5 worth of unleaded, and $0. worth of super-unleaded. To produce a dollar's worth of super-unleaded requires inputs of $0.5 worth of regular, $0.7 worth of unleaded, and $0. worth of super-unleaded. In addition, the oil company has final demands for each of the different grades of gasoline. Find the technology matrix that would be used in determining the total output of each grade of gasoline. 7) 8) The input-output matrix for an economy is Output: Agri. Mfg. Input: Agri. Mfg = T 8) The demand matrix is D = Find the internal consumption

6 9) 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 0.0 of its own output and 0. 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 $6 M demand for electricity and a $7 M demand for gas? Electricity: $5 M; Gas: $0.5 M Electricity: $97.5 M; Gas: $0 M Electricity: $5 M; Gas: $9.5 M Electricity: $07.5 M; Gas: $00 M 0) Two sectors of a textbook economy are () communication equipment and () components and accessories. In 005 the input-output table involving these two sectors was as follows. To Equipment Components From Equipment 6, Components,000 0,000 Total Output 90,000 0,000 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. Equipment: 90,000 Equipment:,000 Components: 0,000 Components: 0,000 Equipment: 86,000 Components: 0,000 Equipment: 86,000 Components: 90,000 9) 0) 6