Neco 2024 Further Mathematics Question 33
Practice objective / multiple choice question 33 from the 2024 Neco Further Mathematics examination.
Let \(T:\mathbb{R}^{2}\to\mathbb{R}^{2}\) be a linear transformation represented by the matrix \(A=\begin{pmatrix} a&b\\ c&d\end{pmatrix}\). It is known that \[T\begin{pmatrix}1\\2\end{pmatrix}=\begin{pmatrix}3\\5\end{pmatrix},\qquad T\begin{pmatrix}2\\-1\end{pmatrix}=\begin{pmatrix}k\\4\end{pmatrix}.\] Moreover, the line \(y=x\) is invariant under \(T\) (any vector on this line is mapped to another vector on the same line). Determine the value of \(k\) and the determinant of \(A\).
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About This Question
This is Neco 2024 Further Mathematics Question 33. It is one of the objective questions from the 2024 Neco Further Mathematics examination.
Difficulty level: Hard .
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