205k views
0 votes
In exercises 15–18, find the values of k for which the matrix a is invertible?

User Chrysillo
by
8.4k points

1 Answer

5 votes

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.

User Nbroeking
by
7.7k points