A linear transformation $T$ in $\mathbb{R}^2$ is represented by the matrix $A=\begin{pmatrix}a&b\c&d\end{pmatrix}$. It maps $(1,2)$ to $(3,5)$ and maps $(2,-1)$ to $(k,4)$. If the area of the unit square after the transformation is $6$, find the possible values of $k$.

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k = \frac{42}{5} 	ext{ or } k = -\frac{18}{5}

Neco 2024 Further Mathematics Question 47

A linear transformation \(T\) in \(\mathbb{R}^2\) is represented by the matrix \(A=\begin{pmatrix}a&b\\c&d\end{pmatrix}\). It maps \((1,2)\) to \((3,5)\) and maps \((2,-1)\) to \((k,4)\). If the area of the unit square after the transformation is \(6\), find the possible values of \(k\).

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