Numerical Methods with Programming

n = 28;
u = 1:n;
v = n:-1:1;
disp(u*v')

Explanation. Recall from Section 1.3 that a:h:b means a regularly spaced vector whose entries start with a, and then change by amount h until reaching b. When h is omitted, it is understood to be 1. So, this code makes u equal to [1 2 ... 28] and v equal to [28 27 ... 1]. Both are row vectors. Transposing the second vector into a column is necessary for their product to make sense, as noted in Section 1.4. Note that each of these lines ends with a semicolon, which prevents the intermediate results from being displayed on screen. Then disp displays the final result.

v = ones(1, 25);
v(2:2:end) = 4;
v(3:2:end-2) = 2;
disp(v)

Explanation. The first line creates a vector of 25 ones, the second changes its even-numbered entries to 4, the third changes odd-numbered entries (except the first and last) to 2. Re-read Section 1.5 if this is unclear.

A = zeros(8, 8);
A(1:2:end, 1:2:end) = 1;
A(2:2:end, 2:2:end) = 1;
disp(A)

Explanation. The first line creates an 8×8 matrix of zeros. The second works with the entries where both the row number and column number are odd, changing them to 1. The third does the same when both row and column numbers are even. The result is a checkerboard.