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This is the Exam of Linear Algebra which includes Encouraged, Vectors, System, Method, Factorization, Square Matrices, Throughout, Invertible, Symmetric etc. Key important points are: Encouraged, Vectors, System, Method, Factorization, Square Matrices, Throughout, Invertible, Symmetric, Reflection Matrix
Typology: Exams
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This take-home exam is due at class time on Monday, October 8. (Sooner is fine.) You may consult the textbook (or any other book) and any class notes and handouts, but please do not discuss any details of this exam with anyone except me! Please sign the bottom of this sheet and turn it in with your exam. You may ask me questions about the exam, but I reserve the right to give unsatisfying answers. Please show all work (though you are encouraged to check your answers on MATLAB or a calculator).
and
x 1 x 2 x 3
(^) by any method (by hand).
(b) Use your answer to (a) to solve A~x =
(c) Find L−^1 and U −^1. Please show work for at least one of these.
(d) Use your answers to (c) to compute A−^1.
(i) Show by an example that BA need not equal O. (You should be able to find a 2 × 2 example, though you are welcome to give a larger example instead.)
(ii) If A is invertible, must BA = O? Explain. What if B is invertible?
(iii) If A and B are symmetric (i.e., A = AT^ and B = BT^ ), prove that BA = O.
I affirm that I did not receive help from another person in doing this exam, nor did I give help to another student in the class.
(signed)