Chapter 9 · Test 2
Determinants & Inverses
Determinants, inverse matrices, nonsingularity, and Cramer's rule.
What you will learn
- Calculate a 2 × 2 determinant
- Compute an inverse-matrix entry
- Solve a nonsingular system
Reasoning habits that help
- A nonzero determinant means the matrix has an inverse and its associated square system has a unique solution.
- For a 2 × 2 inverse, the original top-left entry becomes the inverse's bottom-right entry after division by the determinant.
- Cramer's rule and elimination produce the same unique solution when the coefficient determinant is nonzero.
Where economists use these methods
- Determinants indicate whether simultaneous economic equations have a unique solution and whether a transformation is invertible.
- Inverse matrices recover endogenous variables from structural equations and appear throughout linear econometric models.
- Cramer's rule expresses equilibrium variables as functions of model coefficients, supporting comparative-statics analysis.