Practice question · Multiple choice
The determinant of a 2×2 matrix is the area of the parallelogram its columns span, and it can be negative. What does a negative area mean?
Hints
- Swap the two columns. The shape is identical, what changed?
- Ask whether the transformation could be performed by sliding the plane, or whether it must be lifted and turned over.
Show the answer
B. That the transformation reverses orientation, flipping the plane
Why
The magnitude is area and the sign is handedness: a negative determinant means the plane has been flipped, which no amount of rotating and stretching achieves. It is why a mirror image cannot be rotated onto the original, and why orientation matters in graphics for deciding which face of a surface you are seeing.
Practise Determinants
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