Download Math2341 Summer 2020 Test 2: Matrix, Laplace, Linear Systems, Diff. Equations and more Quizzes Mathematics in PDF only on Docsity!
MATH2341 Summer 2020 Test 2 June 4-5, 2020
Name:
Question: 1 2 3 4 5 6 7 8 9 Total Points: 10 15 7 7 7 15 14 10 15 100 Score:
- (10 points) Let A be a 9 × 9 matrix whose determinant is equal to 43. Answer the following questions based on this information. No partial credit. You don’t have to write any stories justifying your answer. (a) How many solutions will the system Ax = b have for b 6 = 0?
(b) What is the rank of A?
(c) What is the solution of the system Ax = 0?
(d) How many basic variables will you find if you reduced this matrix to its Row Echelon Form (REF)?
(e) How many free variables will you find if you reduced this matrix to its Row Echelon Form (REF)?
- (15 points) For the following questions, circle the letter(s) corresponding to the correct answer(s). All and only correct answers should be picked for each part for credit. No partial credit. (a) Which of the following is the inverse Laplace transform of F (s) = (^2) se 2 −+36^3 ss? A. 2u(t − 3) cos 6(t − 3) B. 13 u(t − 3) sin 6(t − 3) C. 2u(t − 3) sin 6(t − 3) D. 2δ(t − 3) cos 6(t − 3) E. 2δ(t − 3) sin 6(t − 3) F. None of the above
(b) Which of the following matrix multiplication(s) is(are) possible to find the product AB? Circle all possible correct choices for credit and only those which are correct. A. A is a 1 × 3 matrix and B is a 3 × 1 matrix B. A is a 2 × 2 matrix and B is a 3 × 3 matrix C. A is a 2 × 3 matrix and B is a 2 × 3 matrix D. A is a 5 × 7 matrix and B is a 7 × 12 matrix E. A is a 1 × 7 matrix and B is a 7 × 1 matrix F. None of the above will work for AB
(c) For the function f (t) = 3u(t − 2) + 5u(t − 5) − 8 u(t − 9) + 12u(t − 15), what is the value of f (10)? A. 0 B. 24 C. 8 D. 5 E. Cannot be determined without a differential equation F. None of the above
All work should be shown. Copying answers from a calculator without showing work will get 0 points. No exceptions.
- (7 points) Find the value of h for which the following system has a solution (means the system is consistent). (^)
x 1 x 2 x 3
h
- (7 points) Find the values of k for which the following matrix is invertible.
A =
1 k 2 1 2 1 1 2 1 2 1 1
- (15 points) Write the solution to the following homogeneous system in vector form:
x 1 + 2x 2 − 3 x 3 + x 4 + x 5 = 0 −x 1 −x 2 + 4 x 3 −x 4 + 6x 5 = 0
− 2 x 1 − 4 x 2 + 7 x 3 −x 4 + x 5 = 0
- (14 points) Solve the initial value problem y′′^ − 16 y = 32u(t − 2) with y(0) = y′(0) = 0.
- (15 points) Find A−^1 using Gauss Jordan method to find the unique solution to the
linear system
x 1 x 2 x 3
