(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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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