filtering - Short way to eliminate a list from a matrix, if the first element is negative

I'm looking for a short way to eliminate a list from a matrix, if the first element of the list is negative. I've come up with this:

a = {{5, -1, 3, -2}, {-4, -3, -3, -4}, {2, -1, 5, 5}}

f[x_] := Table[x, 4];
Pick[a, f /@ UnitStep[a[[All, 1]]], 1] /. {} -> Nothing

The output is and should be:

{{5, -1, 3, -2}, {2, -1, 5, 5}}

In my example, all lists have a length of 4, this explains the Table[x, 4]. A general case would be more interesting.

Answer

Pick[a,#>=0&@@@a]

{{5, -1, 3, -2}, {2, -1, 5, 5}}

Comments

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