Exam 4: Systems of Linear Equations and Matrices

The U.S. House of Representatives has 178 members. If an appropriations bill passes the House with 40 more members voting in favor than against, how many voted for and how many voted against __________ voted for and __________ voted against.

The Fancy French Perfume Company recently had its secret formula divulged. It turned out that it was using, as the three ingredients, rose oil, oil of fermented prunes, and alcohol. Moreover, each 20-ounce econo-size bottle contained 3 more ounces of alcohol than oil of fermented prunes, while the amount of alcohol was equal to the combined volume of the other two ingredients. How much of each ingredient did it use in an econo-size bottle ?

Find the solution to the system of equations. 9y+2x =1 9x+y =44

Use technology to solve the system of equations. Express all solutions as fractions. ​ 4x-2y+z+v =100 3y+3z-4v =10 2x+4y-v =20 x+3y+3z =10

Use technology to solve the system of equations. Express all solutions as decimals, rounded to one decimal place. ​ 1.6x+2.4y-3.2z=17.6 5.1x-6.3y+0.6z=-12.8 4.2x+3.5y+4.9z=40.4

Use Gauss-Jordan reduction to solve the system of equations. ​ 4x+9z =-2 7y+2z =-4 y+z =-2 ​ If the system is dependent or inconsistent, indicate this.

Use Gauss-Jordan row reduction to solve the given system of equations. ​ x+y+z+u+v =15 y+z+u+v =1 x+2y+2z+2u+2v =16 x-y-z-u-v =13 x-2y-2z-2u-2v =12

Conan the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 545 victims consists of evil sorcerers, warriors, and orcs. These he has slain with a total of 580 mighty thrusts of his sword--evil sorcerers and warriors each requiring 2 thrusts (to the chest) and orcs each requiring 1 thrust (to the neck).When asked about the number of warriors he has slain, he replies, "The number of warriors I, the mighty Conan, have slain is four times the number of evil sorcerers that have fallen to my sword!" How many of each type of villain has he slain Evil sorcerers: __________ Warriors: __________ Orcs: __________

Boeing 747s seat 400 passengers and are priced at $200 million each, Boeing 777s seat 300 passengers and are priced at $160 million, and European Airbus A321s seat 200 passengers and are priced at $60 million. You are the purchasing manager of an airline company and have a $7,920 million budget to purchase new aircraft to seat a total of 19,000 passengers. Your company has a policy of supporting U.S. industries, and you have been required to spend twice as much on U.S.- manufactured aircraft as on foreign aircraft. Given the selection of three aircraft, how many of each should you order Number of Boeing 747s __________ Number of Boeing 777s __________ Number of European Airbus A321s __________

Electric current measures (in amperes, or amps) the flow of electrons through wires. Like traffic flow, the current entering an intersection of wires must equal the current leaving it. Here is an electrical circuit known as a Wheatstone bridge: $a = 5$ A, $b = 20$ A If the currents in two of the wires are 20 amps and 5 amps as shown, determine the currents in the unlabeled wires in terms of suitable parameters.

Use technology to solve the system of equations. 4x-2y+z+v =90 3y+3z-4v =9 2x+4y-v =18 x+3y+3z =9

Solve the system of equations using Gauss-Jordan row reduction. x+y+z+u+v =30 y-z+u-v =-1 z+u+v =16 u-v =-2 v =7

The U.S. House of Representatives has 435 members. If an appropriations bill passes the House with 51 more members voting in favor than against, how many voted for and how many voted against ?

If the addition or subtraction of two linear equations gives the results: $f = 8$ , Then the graphs of those equations will have a relationship to each other that can be described as follows.

Significant numbers of tourists traveled from North America and Asia to Australia and South Africa. In any year a total of 2,223,240 of these tourists visited Australia, and 393,860 of them visited South Africa. Also, 639,210 of these tourists came from North America, and a total of 2,617,100 tourists traveled from these two regions to these two destinations. (Assume that no single tourist visited both destinations or traveled from both North America and Asia.) The given information is not sufficient to determine the number of tourists from each region to each destination. If you were given the additional information that 190,000 tourists visited South Africa from Asia, would you now be able to determine the number of tourists from each region to each destination If so, what are these numbers ?

Use Gauss-Jordan row reduction to solve the given systems of equation. 0.5x+0.1y =0.94 0.1x-0.1y =0.14 x+y =

Use Gauss-Jordan reduction to solve the system of equations. ​ -x-y+z=3 9y-3z=0 z=6 ​ If the system is dependent or inconsistent, indicate this.

Use Gauss-Jordan row reduction to solve the given system of equations. ​ ​ x-y+z-u+v =0 y-z+u-v =-8 x-2v =-8 2x-y+z-u-3v =-8 4x-y+z-u-7v =-24

A system of three equations in two unknowns corresponds to three lines in the plane. Describe how these lines might be positioned if the system has no solutions ?

If the addition or subtraction of two linear equations results in the equation $3 = 3$ , then the graphs of those equations intersect in a single point.