Chapter 10 established the observation-by-sensor structure: we could name its axes, select and reshape it, summarize it, and inspect storage relationships. Here we switch to smaller values while keeping the same `(3, 2)` structure, so each calibration and centered score can be checked by hand.
We begin by applying one calibration formula at every position. Per-sensor and per-observation values then introduce broadcasting through named axes rather than abstract shape tricks. A reduction and a broadcast work together to center each sensor column, with the result checked against a hand calculation and a near-zero mean.
A loop serves as a reference for the whole-array expression. From there, visible products and sums build one weighted score and then several scores. The final lesson checks the complete pipeline for expected shapes, axis meanings, finite values, centered means, and one result calculated by hand. Formal linear algebra comes later; this chapter keeps the executable calculation inspectable.