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this gives a LAPACKException because A is singular and QRFactorization defaults to NoPivot instead of ColumnNorm.
using LinearSolve
A = vcat(rand(1,2), zeros(2,2)), rand(3))
solve(LinearProblem(A, QRFactorization())
I'm not sure if there's a good way to detect whether the factorization is singular in this case, but we should do so and return a failure rather than throw an error.