The matrix $A = \begin{pmatrix} k & 2 \ 3 & k \end{pmatrix}$ is singular. Find the values of k.

Question

Accepted Answer

$k = \pm \sqrt{6}$. A matrix is singular when its determinant equals zero. det(A) = k² - (2)(3) = k² - 6 = 0, giving k² = 6, so k = ±√6. Option A incorrectly solves k² = 36, while option D confuses the entries.

Answer

A) $k = \pm 6$

Answer

B) $k = \pm \sqrt{6}$

Answer

C) $k = 6$ only

Answer

D) $k = \pm 3$

The matrix $A = \begin{pmatrix} k & 2 \\ 3 & k \end{pmatrix}$ is singular. Find the values of k.

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