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