A linear transformation $T:\mathbb{R}^{2}\to\mathbb{R}^{2}$ is represented by a matrix $A=\begin{pmatrix}a&b\c&d\end{pmatrix}$. It satisfies $T(1,2)=(3,5)$ and $T(2,-1)=(k,4)$. Find the value of $k$ for which $\det A =2$. Then compute $T(4,1)$.

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(k = \frac{22}{5},\; T(4,1)=\left(\frac{244}{25},\;\frac{58}{5}\right))

Neco 2019 Further Mathematics Question 12

A linear transformation \(T:\mathbb{R}^{2}\to\mathbb{R}^{2}\) is represented by a matrix \(A=\begin{pmatrix}a&b\\c&d\end{pmatrix}\). It satisfies \(T(1,2)=(3,5)\) and \(T(2,-1)=(k,4)\). Find the value of \(k\) for which \(\det A =2\). Then compute \(T(4,1)\).

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