A linear transformation $T:\mathbb{R}^{2}\to\mathbb{R}^{2}$ satisfies $T(1,2) = (3,5)$ and $T(2,-1) = (0,4)$. Find the matrix $A$ representing $T$ with respect to the standard basis, then determine the determinant of $A^{-1}$. Express $A$ in fractional form.

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A = [[3/5, 6/5],[13/5, 6/5]], det(A^{-1}) = -5/12

Gce Model Questions Vol1 2025 Further Mathematics Question 10

A linear transformation \(T:\mathbb{R}^{2}\to\mathbb{R}^{2}\) satisfies \(T(1,2) = (3,5)\) and \(T(2,-1) = (0,4)\). Find the matrix \(A\) representing \(T\) with respect to the standard basis, then determine the determinant of \(A^{-1}\). Express \(A\) in fractional form.

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