How to extract a vector from a matrix with indices?

Create a linear index with sub2ind, and use it to get the elements you want:

M = randi(99, 3, 2)                                             % Create Matrix
linidx = sub2ind(size(M), 1:size(M,1), [1 2 1])                 % Linear Index
Out = M(linidx)

M =
    95    15
    49    42
    80    91

Out =
    95    42    80