(1 – $1) r1 S1 (1 – s2) r2 G = S2 (1 – s3) r3 (1 – 84) Ta - S3 Here the variables s; represent matriculation (advancing to the next academic class or graduating) while the variables rị represents the retention of students who did not advance but will return to school in the next year. a) Write the characteristic polynomial for this matrix - but do not expand the polynomial. b) One source of college recruitment is the success of its graduates who then interact with future students. Suppose every graduating student recruits R students for the next freshman class. How does this change the matrix G? c) Write the characteristic polynomial for this new matrix - again do not expand the polynomial. d) If s1 = .6, s2 = .7, s3 = .8, and s4 students must a graduate recruit for the school to sustain or increase its enrollment? [Hint: when is 1 an eigenvalue?] = .85, and ri = .5, r2 = .6, r3 : .9, and r4 = .95, how many

(1 – $1) r1 S1 (1 – s2) r2 G = S2 (1 – s3) r3 (1 – 84) Ta - S3 Here the variables s; represent matriculation (advancing to the next academic class or graduating) while the variables rị represents the retention of students who did not advance but will return to school in the next year. a) Write the characteristic polynomial for this matrix - but do not expand the polynomial. b) One source of college recruitment is the success of its graduates who then interact with future students. Suppose every graduating student recruits R students for the next freshman class. How does this change the matrix G? c) Write the characteristic polynomial for this new matrix - again do not expand the polynomial. d) If s1 = .6, s2 = .7, s3 = .8, and s4 students must a graduate recruit for the school to sustain or increase its enrollment? [Hint: when is 1 an eigenvalue?] = .85, and ri = .5, r2 = .6, r3 : .9, and r4 = .95, how many

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

See similar textbooks