Let $ T $ be a linear transformation in $ \mathbb{R}^{2} $ represented by the matrix $ A = \begin{pmatrix} a & b \ c & d \end{pmatrix} $. It is known that $ T(1,2) = (3,5) $, $ T(2,-1) = (k,4) $, and that $ \det A = 7 $. Find the value of $ k $ and then compute $ T(4,1) $.

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k = 47/5; T(4,1) = (419/25, 58/5)

Neco 2020 Further Mathematics Question 13

Let \( T \) be a linear transformation in \( \mathbb{R}^{2} \) represented by the matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \). It is known that \( T(1,2) = (3,5) \), \( T(2,-1) = (k,4) \), and that \( \det A = 7 \). Find the value of \( k \) and then compute \( T(4,1) \).

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