Matrix $ A = \begin{pmatrix} a & b \ c & d \end{pmatrix} $ maps vector $ (1,2) $ to $ (3,5) $ and maps vector $ (2,-1) $ to $ (k,4) $. Find the integer value of $k$ for which the trace of $A$ equals its determinant, and then give that determinant.

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k = 7, determinant = \frac{23}{5}

Neco 2019 Further Mathematics Question 1

Matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) maps vector \( (1,2) \) to \( (3,5) \) and maps vector \( (2,-1) \) to \( (k,4) \). Find the integer value of \(k\) for which the trace of \(A\) equals its determinant, and then give that determinant.

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