Practice question · Multiple choice
A 2×2 matrix has . It transforms the plane. What does it do to the unit square?
Hints
- The determinant is the area scale factor of the transformation.
- Scaling area by zero leaves no area at all. What two-dimensional shapes have zero area?
Show the answer
B. Flattens it onto a line
Why
Zero determinant means total collapse: the square is squashed flat, dimensions are lost, and distinct points pile onto each other. That is exactly why the matrix cannot be inverted, you cannot un-flatten a pancake back into its original points.
Practise Determinants
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