Exam 4: Systems of Linear Equations and Matrices

Use Gauss-Jordan row reduction to solve the given system of equations. ​ 5x-y=14 5x+8y=23

In March 2002 Cisco (CSCO) stock rose from $24 to $25, and America Online-Time Warner (AOL) dropped from $39 to $38. If you invested a total of $19,800 in these stocks at the beginning of March and sold them for $20,100 at the end of March, how many shares of each stock did you buy __________ shares of Cisco __________ shares of America Online-Time Warner

If the addition or subtraction of two linear equations results in the equation $0 = 9$ , then the graphs of those equations are perpendicular.

Find all the solutions (if any) of the given system. ​ 5x-y =-5 7x-3y =-13 ​ If the equations of the system are redundant, or if a system is inconsistent, so indicate.

Big Red Bookstore wants to ship books from its warehouses in Brooklyn and Queens to its stores, one on Long Island and one in Manhattan. Its warehouse in Brooklyn has 1,000 books and its warehouse in Queens has 2,000. Each store orders 1,500 books. It costs $1 to ship each book from Brooklyn to Manhattan and $2 to ship each book from Queens to Manhattan. It costs $5 to ship each book from Brooklyn to Long Island and $4 to ship each book from Queens to Long Island. a. If Big Red has a transportation budget of $9,200 and is willing to spend all of it, how many books should Big Red ship from each warehouse to each store in order to fill all the orders Brooklyn to Manhattan __________ Queens to Manhattan __________ Brooklyn to Long Island __________ Queens to Long Island __________ b. How many books should Big Red ship from each warehouse to each store in order to fill all the orders for the minimum amount of money Brooklyn to Manhattan __________ Queens to Manhattan __________ Brooklyn to Long Island __________ Queens to Long Island __________

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

The best sports dorm on campus, Lombardi House, has won a total of 7 games this semester. Some of these games were soccer games, and the others were football games. According to the rules of the university, each win in a soccer gamer earns the winning house 3 points, whereas each win in a football game earns them 7 points. If the total number of points Lombardi House earned was 41, how many of each type of game did they win ?

This exercise is based on the following simplified model of the determination of the money stock. M=C+D C=0.2D R=0.1D H=R+C , Where M - money stock C - currency in circulation R - bank reserves D - deposits of the public H - high-powered money If the money stock were $192 billion, what would bank reserves have to be

Find all the solutions (if any) of the given system. ​ ​ y-8x=0 4x+3y=7 ​ If the equations of the system are redundant, or if a system is inconsistent, so indicate.

In November 2003, the four companies with the largest number of home Internet users in the US were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 274 million users. Taking $\chi$ to be the Microsoft audience in millions, $y$ the Time Warner audience in millions, $Z$ the Yahoo audience in millions, and $u$ the Google audience in millions, it was observed that z-u=3(x-y)+6 x+y=56+z+u x-y+z-u=50 How large was the audience of each of the four companies in November, 2003 (All amounts in millions.)

Use Gauss-Jordan row reduction to solve the given system of equations. x-y=6 x+y+z=6 x-z=-1