inv returns wrong result for this SymTridiagonal([1., 0., 0.], [0., 1.])

```julia
julia> using LinearAlgebra
julia> A = SymTridiagonal([1., 0., 0.], [0., 1.])
3×3 SymTridiagonal{Float64,Array{Float64,1}}:
1.0 0.0 ⋅
0.0 0.0 1.0
⋅ 1.0 0.0

julia> inv(A)
3×3 Array{Float64,2}:
NaN NaN NaN
NaN NaN NaN
NaN NaN NaN

julia> inv(convert(Array, A))
3×3 Array{Float64,2}:
1.0 -0.0 -0.0
0.0 -0.0 1.0
0.0 1.0 0.0

julia> versioninfo()
Julia Version 1.1.0
Commit 80516ca202 (2019-01-21 21:24 UTC)
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: Intel(R) Core(TM) i5-7200U CPU @ 2.50GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-6.0.1 (ORCJIT, skylake)
Environment:
JULIA_EDITOR = "C:\Users\wangc\AppData\Local\atom\app-1.34.0\atom.exe" -a
JULIA_NUM_THREADS = 2
```

Reproduce the Julia snippet using SymTridiagonal and compare inv(A) with inv(convert(Array, A)). Trace the inv path for SymTridiagonal and determine why the result differs from the dense conversion; the example is the validation target, and done means inv(A) returns the expected inverse rather than an all-NaN matrix.

Written by the indexing model from the issue text.