Question

The figure to the right gives the responses of a group of 100 randomly selected college freshmen when asked for the highest academic degree that they intended to obtain. Twice as many students intended to obtain master's degrees as their highest degree than intended to obtain bachelor's degrees as their highest degree. The number of students intending to obtain bachelor's or master's degrees as their highest degree was 2 more than the number who intended to obtain other degrees as their highest degree. Let x, y, and z represent the number of students that intend to obtains a master's degree, bachelor's degree, or other respectively). Use the Gauss-Jordan method for calculating inverses to determine the values of x, y, and z. Click the icon to view the bar graph of highest academic degree intended to obtain. 0 Bar Graph - X Find the inverse of the coefficient matrix formed by writing the given information in three equations. (Type an integer or simplified fraction for each matrix element.) LI Print Done

Answer 1

het a number of students that intend to obtain a master's degree. y= number of stedents that intend to obtain a bachelor's degree. za number of students that intend to obtain other degras. given, total number of students a 100 →x+y+zlow --- • given, twice as many students intended to obtain master's degrees as their highest degree than intended to obtain bachelor's degrees as their highest degree. x=24 *- - 0 --- 01) Number of students intending to obtain master's degree or bachelor's degree as their highest degree was a more than the number who intended to obtach other degrees. hty=2+2 *+/-2 -2 ----Uri) The required linear system is hty+z=100 n-2y =o xty -2=2 • lii ] LAME 5 where Al 17 Il 1- Using Gauss. Jordan method to obtain inverse of A=IA i 11/ 01 1 -2 0/ A A 11. 07 10 -3 11 uloA RRER LO Rza RR,

- - o R 11/322 - oo - [² o į J B - 2 R3 o 13 bol om o amamo - o R=R-R coo - wt we – wt 0 o ( 3 - 3 o 0 | |% - R R-33R3 R₂R 1R % | A 0 o ; -m-1 o wr wil um 16 W • Añ=5 R=ÀI ME o o wr wie -/m te tv o dim dhe to- - ..1=34 J=17 Z=49 Ν