Checklist USA-NA-AIO 2026 Round 1 · Task 3
Matrix of a Linear Map and Rank-One Decomposition
Recover a 3×4 matrix from its action on a vector and write it as a sum of outer products.
The task
Problem 3 (10 points) defines A in R^{3×4} by Ax = (x2 − x3, x3, x0 + 2x1). Part 3.1 asks for A; Part 3.2 asks for a decomposition A = Σ_i u(i) v(i)^T, stating the number of terms and the vectors, with reasoning.
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
- Written answers.
- Format
- 2026 USA-NA-AIO Round 1, 30 January 2026 (date printed on the problem set). Individual, proctored.