gibson:teaching:fall-2013:math445:exam1solns

**1.** Write one line of Matlab code that returns the 4th column of
the matrix .

A(:,4)

**2.** Write Matlab code that sets all entries in the 3rd row of the
matrix to zero. Its possible to do this in one line, but you can use several.

A(3,:) = 0;

or

A(3,:) = zeros(1,size(A,2));

or

[M,N] = size(A); A(3,:) = zeros(1,N);

**3.** Write one line of Matlab code for an anonymous function that
computes the value of the polynomial for an input argument .

f = @(x) 3*x^2 - 2*x - 7;

**4.** How would you use Matlab and the anonymous function from
problem 3 to find a numerical solution to the equation ?
One line of code should do it.

x = newtonsearch(f,2);

or

x = fzero(f,2);

Note: 2 is an initial guess for the solution, chosen because f(2) = 1 (this is relatively close to zero).

**5.** Write one line of Matlab code that evaluates to 1 (true) if
is negative and is positive, and 0 (false) otherwise.

x < 0 && y > 0

**6.** Write one line of Matlab code that evaluates to 1 (true) if
both and are positive or if both are negative, and 0 (false) otherwise.

(x < 0 && y < 0) || (x > 0 && y > 0)

**7.** Write one line of Matlab code that counts how many components
of the vector are exactly zero.

sum(v==0)

**8.** Show how to solve the system of equations with three lines of Matlab code.

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 according to the formula

where 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 transition
matrix for a network of web pages and returns the page rank vector
of the steady-state distribution of visitors to each page. The page rank is
given by , where is an arbitrary -vector whose components
sum to 1, and is large number. You can set 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

gibson/teaching/fall-2013/math445/exam1solns.txt · Last modified: 2013/10/29 06:14 by gibson