Science:Math Exam Resources/Courses/MATH152/April 2015/Question A 10
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Question A 10 

Consider the following lines of MATLAB code: A = zeros(10, 10); for i=1:9 A(i, i) = 1/2; A(i+1, i) = 1/2; end A(10, 10) = 1; Circle the answer below that best describes the resulting matrix :

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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Recall the following definitions:

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We see from the first line A = zeros(10, 10); that is initialized as a 10by10 matrix of zeroes. In the first iteration of the loop (when i = 1), we set and the entry below it, , to also. Continuing in this manner for , at the end of the loop we obtain where the last two entries modified by the loop are and . We finally set , forming the matrix
which is seen to be leftstochastic, and hence (b) the transition matrix for a random walk. 