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- 4. Problem(4)(weight30%)TrueorFalse?(Ifthegivenstatementistrue,provideaproof,butifthestatementisfalse,giveTWO examples showingthatitisfalse.)(a) Asystemoflinearequationswithfewerequationsthanvariablescannot haveauniquesolution.(b) Forvectors ~a, ~b and ~c, if ~a ~b = ~a ~c and ~a 6= ~0 then ~b = ~c.2. Problem(2)(weight20%)Find thevaluesof for whichthedeterminantiszero.0@ + 1004 42 6 + 5In Problems 29-33, a survey of freshman calculus students at a certain university showed the following graphics calculator use: 21 use TI 45 use Casio 24 use HP 1 uses none of the above 13 use TI and Casio 14 use HP and TI 15 use Casio and HP 8 use all three of the above 29. How many students were surveyed? 30. How many of the Casio users do NOT use TI? 31. How many students use at least one calculator besides Casio? 32. How many students use at most two of the calculators?
- Problem #3 A through FIf a machine has an efficiency rating of 0.4 and is replaced by another machine with an efficiency rating of 0.34, will the new machine be as efficient? (a) Yes (b) No (c) Cannot be determined from the information givenRework problem 4 in section 3 of Chapter 5 of your textbook using the following data. Assume that each gallon of Deluxe Vanilla uses 2 quarts of milk, 2 quarts of cream, and 3 ounces of vanilla; each gallon of Regular Vanilla uses 3 quarts of milk, 1 quart(s) of cream, and 2 ounces of vanilla; and each gallon of Deluxe Chocolate uses 3.5 quarts of milk, 0.5 quarts of cream, and 7 ounces of cacao. Assume also that the shop has on hand 124 gallons of milk, 68 gallons of cream, 23 pounds of vanilla, and 28 pounds of cacao. How many gallons of each type of ice cream should the shop make to use up all of these ingredients? When you setup a system of linear equations to solve this problem, how many variables and how many equations should you have.?Number of variables: Number of equations:
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