1. Write one line of Matlab code that returns the 4th column of the matrix .
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;
A(3,:) = zeros(1,size(A,2));
[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);
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.
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