Checklist USA-NA-AIO 2026 Round 1 · Task 2
Projection onto a Principal Component
Compute a unit principal direction, a projection and its residual for small vectors.
The task
Problem 2 (15 points) gives a data point x in R^d and a unit-length principal component e. For d = 3 the contestant normalises v = (1, −2, 3), projects x = (−1, −4, 6) onto the direction, and computes the residual; each answer is encoded as an integer expression chosen from five options.
Abridged by SOTA from the official materials. The official statement has the exact rules, and it wins wherever this summary differs.
At a glance
- You submit
- One option (A–E) per part (three parts of 5 points).
- Format
- 2026 USA-NA-AIO Round 1, 30 January 2026 (date printed on the problem set). Individual, proctored.