AME404SampleMidterm

AME404SampleMidterm - y is an n& vector(b Draw the...

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AME 404 Midterm Exam Place: MHP 101. Time: 11-12:20. Date: October 6, 2004 Professor: M. Dravinski Name Instructions. Closed books and notes. No calculators or computers. 1. (30 Pts.) (a) Using Gauss elimination with partial pivoting perform LU-decomposition of matrix A , i.e., °nd the permutation matrix P ; upper triangular matrix U and lower triangular matrix L such that PA = LU ; where A = 2 4 1 5 5 2 6 5 1 2 2 3 5 (b) Use the results of Part 1A to solve the system of equations Ax = b ; using the LU-decomposition with partial pivoting, where b = [ ° 4 ; ° 5 ; ° 1] 0 . 2. ( 30 Pts.) (a) Derive a solution for an upper triangular system Ux = y ; where U is an upper triangular n ° by ° n matrix and
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Unformatted text preview: y is an n & vector. (b) Draw the ±owchart for a function [x]=backSubst(U,y) which implements the solution of Part 2a on a digital computer. 3. ( 40 Pts.) Assume that the MATLAB functions [L,P,U]=lu(A), [y]=forwardSubst(L,b) and [x]=backSubst(U,y), that perform LU-decomposition, forward and backward substitutions, respectively are given. (a) Explain mathematically how to calculate the inverse of a matrix A using the LU-decomposition. (b) Draw the corresponding ±owchart which implements the procedure outlined in Part 3a on a digital computer. 1...
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