Linear algebra

Determinants, entries of an inverse, whole-number eigenvalues and linear systems on 2 × 2 and 3 × 3 matrices.

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How it works

The question is built by cofactors, adjugates and Cramer’s rule; before it is shown, exact row reduction recomputes the answer, and a search for every λ that makes A − λI singular confirms the eigenvalues. Answers are whole numbers or fractions. DRW and G-Research online tests are reported to include linear algebra.

A sample question

Every eigenvalue of $A = [3 - 2 16]$ is a whole number. What is the largest?