Parameter values for a singular matrix

EasyLinear Algebra~3m

The matrix $\begin{pmatrix} k & 3 \\ 4 & k-1 \end{pmatrix}$ is singular (non-invertible) for two different real values of $k$ . What is the sum of those two values?

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Singular means $\det = 0$ ; here that gives a quadratic in $k$ .
The sum of the roots of $k^2 - k - 12 = 0$ is $-(-1) = 1$ (Vieta).

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Asked at: Multi-Strategy Quant, Data-Driven Research

Parameter values for a singular matrix

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