Add a "Solving linear systems" section to the sparse solvers manual

[ViralBShah]

The solvers page listed the factorizations and their docstrings but had no narrative. This adds a section covering what A \ b and factorize dispatch to (substitution, cholesky with its fallback, lu, qr, and lq for the minimum-norm solution of wide systems), reusing and refactorizing a factorization (F \ B, ldiv!, lu!/cholesky!/ldlt!), extracting factors with the permuted identities they satisfy, and the symmetric-input and check = false/issuccess rules.

The material comes from reading \ and factorize in src/linalg.jl, the Hermitian \ in src/solvers/cholmod.jl, the lu/cholesky/qr/lq docstrings, and #830, #831, #833, #835. One thing the text makes explicit: for a Hermitian matrix that is not positive definite, \ falls back to lu while factorize falls back to ldlt. Every example is a doctest printing only true/false; the Documenter build and doctests pass on nightly with no new warnings. Docs only; tuning keywords and threading are left to a separate PR.

The insertion sits directly above the @docs line that #838 edits, so whichever merges second will need a trivial rebase.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.64%. Comparing base (2a27cf9) to head (8f117fe).
⚠️ Report is 7 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #841      +/-   ##
==========================================
+ Coverage   92.60%   92.64%   +0.04%     
==========================================
  Files          12       12              
  Lines        8727     8721       -6     
==========================================
- Hits         8082     8080       -2     
+ Misses        645      641       -4     

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