Use the determinant to determine whether a square matrix of any order is singular or non- singular.

Consider the matrix A = [[2, 4, 1], [3, -1, 2], [1, 5, k]]. Determine the value of k for which the matrix is singular.

Determine whether the matrix \( A = \begin{pmatrix} 2 & 4 & 1 \\ 1 & 2 & 3 \\ 3 & 6 & 4 \end{pmatrix} \) is singular or non-singular.

Three vectors form the columns of a matrix \[ M = \begin{pmatrix} 2 & 1 & 3 \\ -1 & 4 & 2 \\ 1 & 2 & -1 \end{pmatrix} \] Determine whether the matrix $M$ is singular or non-singular by calculating its determinant. Show your working.