Final answer:
To find the values of k for which the matrix is invertible, calculate the determinant of the matrix and set it equal to zero. In the given example, the matrix A is invertible for all values of k except 1/2.
Step-by-step explanation:
In order for a matrix to be invertible, its determinant must be non-zero. To find the values of k for which the matrix is invertible, we need to calculate the determinant of the matrix and set it equal to zero.
Let's assume the matrix is A = [[a, b], [c, d]]. The determinant of A is given by det(A) = ad - bc.
If we have the matrix A = [[2, k], [4, 1]], then the determinant is det(A) = 2*1 - 4*k = 2 - 4k.
To find the values of k for which the matrix is invertible, we set 2 - 4k ≠ 0 and solve for k: 2 - 4k ≠ 0 => -4k ≠ -2 => k ≠ 1/2.