Practice question · Multiple choice
The determinant’s absolute value is the factor by which a transformation scales area or volume. What does a determinant of zero mean geometrically?
Hints
- Ask what happens to a square’s area under the map.
- Can you recover the square if it has been squashed onto a segment?
Show the answer
C. That it collapses space onto a lower dimension
Why
Zero volume means dimensions were lost, and lost information cannot be restored. Singularity and non-invertibility are the same fact stated algebraically and geometrically.
Practise Determinants
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