Final Exam - Math 2090 Final Exam Spring 2011 Britt Work...

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Chapter 7 / Exercise 20
Elementary Linear Algebra
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Math 2090 Final Exam Spring 2011 Britt Work the problems in order on the fronts of your paper. Show your work. l[ ] 1. Compute the Laplace Inverse L- ') s+2 . s~ + y" y' - 2y -= 6e- , 2. Detennine L[ (t -1/ u 4 (t) 3. Solve the following initial value problem by using Laplace Transfonns yeO) = 0, y'(O) '> (''-LA - , ! ~ 4. Solve the following differentIal equations -3x a) y' -2ysinx b)y,+.ly=e\ x>O c) Y " - X 8 d) y"-4y Hint: Use Variation of Parameters 5. Let A be a non-singular n x n matrix. List three other statements which are equivalent to this fact. 6. Solve the following linear system using Gauss-Jordan reduction. 3x 2y z=4 x+2y z=6 2x+ y+z 7. Compute the inverse ofthe matrix r ~ !i by using row reduction. No other method will , get credit. 8. Detennine if the following are vector spaces. EXPLAIN YOUR REASONING if you are claiming they are not a vector space. 2s + 2 l J = 1 Y = 8 e =9 J A) The set of2x2 matrices with a 0 in position 2,2 with operations defined in the standard manner. B) The set of all increasing functions on JR with operations defined in the usual manner.
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Chapter 7 / Exercise 20
Elementary Linear Algebra
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