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--- gibson:teaching:fall-2013:math445:exam1solns [2013/10/28 13:06]
gibson created
+++ gibson:teaching:fall-2013:math445:exam1solns [2013/10/29 06:14] (current)
gibson
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 </latex>
+  A = [ 3 1 2; -1 0 9; -4 5 0];
+  b = [6; 8; 1];
+  x = A\b
+**9.**  Write a Matlab function that computes the mean (i.e. average) of
+the components of a vector $x$ according to the formula
+<latex>
+  \text{mean}(x) = (1/N) \sum_{i=1}^{N} x_i
+</latex>
+where $N$ is the length of the vector. Your function should evaluate this
+sum directly instead of using the Matlab %%sum%% or %%mean%% functions.
+  function m = mean(x)
+  % compute mean of vector x
+    m = 0;
+    N = length(x);
+    for i=1:N
+      m = m + x(i);
+    end
+    m = m/N;
+  end
+**10.**  Write a Matlab function that takes an $M \times M$  transition
+matrix $T$ for a network of $M$ web pages and returns the page rank vector $p$
+of the steady-state distribution of visitors to each page. The page rank is
+given by $p = T^n e$, where $e$ is an arbitrary $M$-vector whose components
+sum to 1, and $n$ is large number. You can set $n$ to 100.
+  function p = pagerank(T);
+  % compute that page rank vector for transition matrix T
+    [M,M] = size(T);
+    e = zeros(M,1);
+    e(1) = 1;
+    n=100;
+    p = T^n * e;
+  end