Midterm2Solution

# Midterm2Solution - BME 210 Spring 2009 Name MIDTERM...

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BME 210 Spring 2009 Name: _______________________________ MIDTERM EXAMINATION #2 (1 hr 15 min) (5 points) 1. Consider the 9 element pixel grid shown below with the 6 projections indicted. Write down the 6 equations for these projections. When a ray sum goes through a pixel, assume it goes through that pixel’s center and therefore use a value of 1 for the weight for that pixel. S 1 S 2 S 3 S 4 S 5 μ 1 μ 2 μ 3 μ 4 μ 5 μ 6 μ 7 μ 8 μ 9 S 6 178 225 336 43 548 61 S S S S S S 9 8 9 =μ+μ+μ =μ +μ 1

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(15 points) 2. Write a complete MATLAB program that implements the forward substitution algorithm shown below to solve a general n th order lower triangular system. The program should read in the matrix L and vector b from files L.dat and b.dat and should print the solution y. Forward Substitution Algorithm n th Order System Ly=b y 1 = b 1 α 11 y i = 1 ii b i ij y j j = 1 i 1 i = 2, , n 11 1 1 21 22 2 2 1 00 0 nn n n n yb αα ⎤⎡ ⎤ ⎡ ⎤ ⎥⎢ ⎥ ⎢ ⎥ = ⎦⎣ ⎦ ⎣ ⎦ " %# #%# # "" % Midterm 2, Question 2 % Forward substitution clear all close all load L.dat; load b.dat; n=length(b); alpha=L; y(1)=b(1)/alpha(1,1); for i=2:n; sum=0.0; for j=1:i-1; sum=sum + alpha(i,j)*y(j); end y(i)=(b(i)-sum)/alpha(i,i); end y 2
(15 points) 3. The following compartment model has been used to represent the disposition of the an orally administered drug and its metabolite. In the figure below, x i represents the amount of drug in the ith compartment.

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Midterm2Solution - BME 210 Spring 2009 Name MIDTERM...

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