solve doesn't work for non-square matrix over inexact field

This seems not right:

Say we have a random matrix:

i1 : A = random(RR^3, RR^3)
o1 = | .941075 .728174 .559197 |
     | .143775 .110624 .482643 |
     | .531091 .126337 .393081 |

Surely the first column is in the column span of A:

i2 : solve(A, A_{0}) -- this is fine

o2 = | 1           |
     | 8.00436e-17 |
     | 2.8623e-17  |

But somehow there's no answer if we remove the last column?

i3 : solve(A_{0,1}, A_{0}) -- why no answer?

i4 : solve(A_{0,1,0}, A_{0}) -- why no answer?

What's more bizarre, very occasionally the last line above does return an answer:

i14 : A = random(RR^3, RR^3)

o14 = | .915419 .759446 .469346 |
      | .455108 .922644 .920515 |
      | .716856 .999732 .327083 |

                 3         3
o14 : Matrix RR    <-- RR
               53        53

i18 : solve(A_{0,1}, A_{0}) -- why no answer?

i19 : solve(A_{0,1,0}, A_{0}) -- but this works?!?!

o19 = | .498589     |
      | -1.4841e-17 |
      | .501411     |

                 3         1
o19 : Matrix RR    <-- RR
               53        53

The trend is pretty much the flip of a coin:

i53 : tally apply(100, i -> (
      	A := random(RR^3, RR^3);
      	null === solve(A_{0,1}, A_{0}),
      	null === solve(A_{0,1,0}, A_{0})
      	))

o53 = Tally{(true, false) => 41}
            (true, true) => 59

This is not an issue over QQ, but seems to be even more random over CC:

i50 : tally apply(100, i -> (
      	A := random(CC^3, CC^3);
      	null === solve(A_{0,1}, A_{0}),
      	null === solve(A_{0,1,0}, A_{0})
      	))

o50 = Tally{(false, false) => 3}
            (true, false) => 85
            (true, true) => 12