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 𝑥 2 + 𝑦 2 ≤ 1 gets transformed to a region with an area equal to _________ . (Rounded off to two decimals) Use π = 3.14.

GATE Mechanical Engineering (ME) 2023 Shift 1 Solved Paper

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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.

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