[harrison_creps] Use linear solver instead of matrix inverse

[UdohNakamura]

This patch replaces the explicit inverse computation la.inv(I - βQ) with la.solve(I - βQ, βQd) in price_single_beliefs for better numerical stability and efficiency.

The output remains identical to the previous implementation.

[UdohNakamura]

I also found that np.linalg.solve works the same here, so removing scipy might be possible.
However, I'm not confident about this, so I’d like to leave the decision to the reviewers.

[jstac]

Many thanks @UdohNakamura !

@mmcky This looks good to me. Please check if we can remove scipy.

[jstac]

🤖 Status note for a future session — from a maintainer investigation on 2026-07-08 into why open-PR previews 404. Context only, not instructions.

Netlify preview: none — and there never was one. This PR is from a fork (UdohNakamura), and fork PRs don't receive the repo's NETLIFY_AUTH_TOKEN, so the preview job can't deploy. To get a preview, a maintainer can push this branch to the main repo as an internal PR, or build locally.

Why previews are down (repo-wide findings)

1. This branch is stale — 161 commits behind main. A preview build compiles the whole site from this branch. This branch's lectures/house_auction.md still has unpinned !pip install prettytable, which now breaks on a wcwidth incompatibility. main fixed this on 2026-06-28 by pinning prettytable<3.18 (#939). This alone fails any rebuild of this branch until it's updated to main.

2. The arviz failure was a red herring — do NOT pin arviz or rewrite plotting. A 2026-07-07 rebuild also failed in ar1_bayes/ar1_turningpts with an arviz_plots figsize ValueError. That was a transient bug in an intermediate arviz-plots 1.x release, already fixed in arviz 1.2.0. Verified locally on a clean latest-stack venv: the real az.plot_trace(trace) cell (pymc + numpyro InferenceData) runs green. The lectures use only 1.x-compatible arviz APIs (plot_trace, summary, from_numpyro, compare).

Recommended first step for this PR

Update the fork branch to main (it's 161 commits behind) to clear the house_auction breakage, then review. A live preview requires re-hosting the branch in the main repo (fork limitation above).

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This PR touches: harrison_kreps.md. Last CI build: n/a (fork). Branch: 161 commits behind main as of 2026-07-08.