Final answer:
To find the values of k for which the matrix a is invertible, we need to determine the determinant of matrix a and set it equal to zero. Solve for k to find the values for which the matrix a is not invertible.
Step-by-step explanation:
To find the values of k for which the matrix a is invertible, we need to determine the determinant of matrix a. If the determinant is non-zero, then the matrix is invertible. If the determinant is zero, then the matrix is not invertible.
So, calculate the determinant of matrix a and set it equal to zero. Solve for k to find the values for which the matrix a is not invertible.
For example, if the matrix a is given by:
a = [[4, -2], [k, 3]]
Then, the determinant of a is given by:
det(a) = (4)(3) - (-2)(k) = 12 + 2k
Set the determinant equal to zero and solve for k:
12 + 2k = 0
2k = -12
k = -6
Therefore, the values of k for which the matrix a is not invertible are k = -6.