Business I / Determinants
Practice question · Match the pairs

Match each statement to its equivalent.

  • det⁡A≠0\det A \ne 0
  • det⁡A=0\det A = 0
  • ∣det⁡A∣=6|\det A| = 6
  • det⁡A<0\det A < 0
  • The transformation flips orientation
  • Areas are scaled by a factor of 6
  • A−1A^{-1} exists
  • Rows are linearly dependent
Hints
  1. The same number can be read algebraically or geometrically.
  2. Vanishing corresponds to a collapse of area.
Show the answer
  • det⁡A≠0\det A \ne 0 → A−1A^{-1} exists
  • det⁡A=0\det A = 0 → Rows are linearly dependent
  • ∣det⁡A∣=6|\det A| = 6 → Areas are scaled by a factor of 6
  • det⁡A<0\det A < 0 → The transformation flips orientation
Why

One number, four readings: invertibility, dependence, area scaling, and orientation.

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