Practice question · Numerical answer
The matrix with rows (2, 0) and (0, 2) is applied to the plane. By what factor does it multiply areas?
Hints
- The area scaling factor is the absolute value of the determinant.
- Both axes are stretched by 2, and area involves both directions.
Show the answer
4
Why
The determinant is 4, so areas quadruple, a unit square becomes a 2 by 2 square. Doubling every length doubles the area twice over, which is why the scaling factors multiply rather than add.
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