APPM 2360 Midterm: appm2360fall2017exam3

30 views2 pages

turquoisegnu128

31 Jan 2019

School

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

On the front of your bluebook write: (1) your name, (2) your instructor"s name, (3) your lecture section number and (4) a grading table. Text books, class notes, cell phones and calculators are not permitted. Problem 1: (30 points) true/false (answer true if it is always true otherwise answer false. No justi cation is needed. ) (a) if all eigenvalues of a are distinct, then a is invertible. (b) suppose that for functions f (t) and g(t) we have that their laplace transforms l [f (t)](s) and l [g(t)](s) exist. Problem 2: (30 points) short answer for the following problems. No justi cation is needed. (a) (7 points) a system is described by the equation x +3 x +5 x = sin(5 t). Find the frequency of the steady-state solution (i. e. , the frequency of the solution as t ). (b) (7 points) a mass of 1 kg is attached to a spring with constant k = 9 n/m.

Related Questions

3. (7 points) Decide whether the following statements are trueor false (give a short justication if you
want full points!):
(a) A homogeneous system of three equations and four variables hasa nontrivial solution.

(b) If u1; u2 are both solutions to the system Ax = b then(u1+u2)/2 is also a solution.

(d) If A;B;C are nxn non-singular matrices, then (ABC)^-1 =C^-1A^-1B^-1

(e) There can be a 4x4 non-singular matrix A such that Ax = 0 has anon-trivial solution (i.e.
x is a solution with some non-zero entries).

(f) Every square matrix with 1's down the diagonal isinvertible

(g) If A is invertible, then A^2 is invertible too.