+.3y = u .1x .7y = v (a) Write this system of equations in matrix form.
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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Statistics show that at a certain university, 90% of the students who live on campus during a given semester will remain on campus the following semester, and 70% of students living off campus during a given semester will remain off campus the following semester. Let x and y denote the number of students who live on and off campus this semester, and let u and v be the corresponding numbers for the next semester. Then the following system of equations can be formed. Complete parts a through c.
| .9x | +.3y | = | u |
| .1x | .7y | = | v |
(a) Write this system of equations in matrix form.
(b) Solve the resulting matrix equation for X=
(c) Suppose that, out of a group of 42,000 students, 24,000 currently live on campus and 18,000 live off campus. How many lived on campus last semester? How many will live off campus next semester?
| x |
| y |
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