Project ForgeEngineering Mathematics
Linear Algebra
GATE 2023
Medium
A linear transformation maps a point (x,y) in the plane to the point (x̂,ŷ) according to the rule x̂=3y, ŷ=2x. Then, the disc x²+y²≤1 gets transformed to a region with an area equal to _____. (Rounded off to two decimals; use π=3.14)
18.84(± 0.1 accepted)
Explanation
The map is [[0,3],[2,0]] applied to (x,y). The area-scale factor under a linear map equals |det|=|0×0−3×2|=6. The unit disc has area π=3.14, so the transformed area = 6×3.14=18.84.
Source: GATE ME 2023 Official Paper (2023)
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