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mid term macm 316 practice and sulo
Typology: Exams
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Instructions: 50 minutes. Answer all 5 questions. Closed book.
One-sided cheat sheet and non-graphing calculator permitted.
Mark very clearly on the question if you use the back of any page.
Do not expect ANY marks for answers that do not provide intermediate work.
Marks may be deducted for poor presentation.
lim h! 0
h cos(h 2 ) sin(h)
Show your steps.
h 1 0 2 1
i , U =
h 4 1 0 2
i , and P =
h 0 1 1 0
i .
(a) Solve the linear system Ax = b where b = [0 2] T^ using the given factorization.
(b) What is the determinant of A in terms of det(L) and det(U )?
iteration matrix for Jacobi’s method. (This tells us that Jacobi’s method converges for any diagonally dominant matrix.)
