Math 166 WIR, Fall 2011,cBenjamin AurispaMath 166 Exam 3 ReviewSections F.1-F.4, 4.3-4.4, & 5.1-5.3Note: This review covers the highlights of these sections. For additional practice problems, take a look atWeek in Reviews 7 and 8.1. Solve for the variables in the following equation.1 −2−4 9−1− 2c + 1 62b aT=−1 −59d 43 01 42. Given the following matrices and their sizes, determine whether the matrix operations are possible ornot possible. If possible, give the dimensions (order) of the resulting matrix.A2×4B3×2C4×3D3×3, nonsingular E2×3F2×2, singular(a) 4AC + E (b) BA + C (c) ATE − 7C (d)F−1A(e) BED−1(f) DBT(g) A−1F1Math 166 WIR, Fall 2011,cBenjamin AurispaA2×4B3×2C4×3D3×3, nonsingular E2×3F2×2, singularTrue or False:(h) I2F = F (i) BI3= B (j) DD−1+ D = D3. John and Bill are both throwing Super Bowl parties and want to order pizzas. Matrix A gives thecost of a small, medium, and large pizza at Papa John’s and Pizza Hut. Matrix B gives the numberof small, medium, and large pizzas that John and Bill want to order for their parties.A=PJ PHSML6 59 1012 13B=J BSML5 23 76 9Which of the following matrix products gives the cost of each person’s order if they ordered at eachstore?• AB • BA• ABT• BTA2Math 166 WIR, Fall 2011,cBenjamin Aurispa4. Matrix X represents the number of cups of sugar and flour per serving of food I and food II. MatrixY gives the number of servings of food I and food II needed for event A and event B.X=Sug FloFIFII3 72 9Y=FI FIIAB12 106 11(a) What is the meaning of the matrix XY ?(b) What is the meaning of the matrix Y X?5. Solve the following matrix equation for X.(Assume all matrix operations are possible and that any necessary inverses exist.)X − XB + E = F6. Solve the following systems of equations. If there are infinitely many solutions, give a parameterizedsolution and a particular solution.(a) 10x − 8y = 6−15x + 12y = 20−25x + 20y = 723Math 166 WIR, Fall 2011,cBenjamin Aurispa(b) x + y + z + u = 52x + 3y − 9z = 183x + 16z + 4u = 17. Suppose there are 3 major airlines that fly out of Houston: Southwest, Delta, and American. ASouthwest flight holds 135 people, a Delta flight holds 160 people, and an American flight holds 148people. On a given day, a total of 88,683 people flew out of Houston. There were 3 times as manySouthwest flights as Delta flights, and the number of American flights was half the number of Southwestand Delta flights combined. How many flights out of Houston were there for each airline if every flightwas full? [Solve your system by creating a matrix equation AX = B and using matrix inverses.]4Math 166 WIR, Fall 2011,cBenjamin Aurispa8. An event center sold student, adult, and senior citizen tickets for a concert. A student ticket cost $40,an adult ticket cost $85, and a senior citizen ticket cost $70. They sold two times as many studenttickets as senior citizen tickets, the amount of money made from adult tickets was 8.5 times the amountof money made from student tickets, and they brought in total revenue of $872,330. How many ticketsof each type were sold?9. A club is making three different candy bags to give away for Halloween. Each Bag A will have 1Tootsie Roll, 2 Snickers, and 4 Twix. Each Bag B will have 3 Tootsie Rolls, 5 Snickers, and 6 Twix.Each Bag C will have 5 Tootsie Rolls, 7 Snickers, and 2 Twix. They have available 82 Tootsie Rolls,134 Snickers, and 148 Twix. If they use all their supply, how many of each type of bag can they make?5Math 166 WIR, Fall 2011,cBenjamin Aurispa10. Farmer Fran invested some money at a simple interest rate of 4%/yr. After 21 months, the accounthas $700 in it. How much was initially invested?11. Farmer Fran has $10,000 to invest. He chooses to invest this money in an account with an interestrate of 2%/yr compounded quarterly.(a) How much interest will he have earned after 7 years?N= PMT=I%= FV=PV= P/Y=C/Y=(b) How many years until his investment doubles?N= PMT=I%= FV=PV= P/Y=C/Y=(c) If the account was compounded continuously instead, how much would he have after the aboveamount of time?12. Farmer Fran wants to save up some money to buy a new tractor. He knows he’ll need $15,000. Heplans to invest some money each month in an account that earns 3.1%/yr compounded monthly sothat he has the $15,000 in 2 years.(a) How much should he put in the account each month?N= PMT=I%= FV=PV= P/Y=C/Y=6Math 166 WIR, Fall 2011,cBenjamin Aurispa(b) How much total interest is earned in the 2 years?(c) How much interest is earned during the 3rd month of the second year?13. When you retire, you will receive $1000 weekly payments for 20 years from an account that earnsinterest at a rate of 4.3%/yr compounded weekly?(a) How much needs to be in the account when you retire?N= PMT=I%= FV=PV= P/Y=C/Y=(b) What is the effective interest rate for this account?14. Farmer Fran put down $10,000 on a $190,000 house and financed the remaining balance with a 15-yearmortgage at an interest rate of 5.4%/yr compounded monthly.(a) What is his monthly payment?N= PMT=I%= FV=PV= P/Y=C/Y=(b) How much will he pay in interest over the 15 years?7Math 166 WIR, Fall 2011,cBenjamin Aurispa(c) What is the outstanding principal after 10 years? What is his equity?N= PMT=I%= FV=PV= P/Y=C/Y=(d) Fill in the partial amortization table for the first two periods below.Period Payment Towards Towards Outstanding EquityInterest Principal Principal0 – –
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