underdetermined system

Hi, sorry, I'm an idiot.. and I know I'm missing something stupid.. 

I thought if we solve an underdetermine system with QR, my soln is:

min ||x|| (L2 sense)  such that Ax = b

then say i have:

w <- matrix(c(1, 5), ncol=2)
sw = 2
qrW = qr(t(w) %*% w)
qr.coef(qrW, t(w) %*% sw)

[,1]
[1,]    2
[2,]   NA

but we also have soln (0, 2/5) which obviously has a smaller distance in L2
than (2, 0). Am I missing something very obvious? Thanks a lot!!!!

- yoooooooooooooooooo

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