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STEP III 1990 question 6 solution
From The Student RoomTSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP III 1990 question 6 solution
So applying the transformations to the vectors (1, 2) and (2, -1), we get (2, 4) and (8, -4), both of which are scalar multiples of the original vectors. The matrix transforms the general point (x, y) to (X, Y) =
Therefore the function
As required. The area is equal to the original area multiplied by the determinant of the matrix transformation. The original area is To find the maximum value of X we find Differentiating implicitly, we get There is a stationary point when Treating the curves equation as a quadratic in Y, we get At the stationary point,
The point (0.6, 0.8) is transformed to the point At this point, The equation of the tangent at this point is therefore Solution by Dystopia. |











is transformed to:
; the determinant is 8. Therefore the area is
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