Reverse-Engineering k From the Inverse

20 pts · 20 coins

Determinants & InversesMedium

Let

$A = \begin{pmatrix} k & 3 \\ 2 & k-1 \end{pmatrix}$

You are told that the entry of $A^{-1}$ in row 1, column 2 is exactly $-\tfrac{1}{2}$ , and that $k > 0$ .

What is $k$ ?

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