Question

Find k such that the matrix M= [ 4 1 2 / 12 -1 3 / 26+k -4 2] is invertible.

Note: In order to get credit for this problem, provide the value of k that makes the matrix invertible, along with any necessary justification or calculations.

Answer 1

To find the value of k that makes the matrix M invertible, set the determinant of M equal to zero and solve for k.

Step-by-step explanation:

To find the value of k that makes the matrix M invertible, we need to determine if the determinant of M is non-zero. If the determinant is zero, then the matrix is not invertible.

To calculate the determinant, we can use the formula for a 3x3 matrix:

determinant(M) = (4*(-1*2) - 1*(12*2) + 2*(12*(-4+k)))

We want to find the value of k such that the determinant is not zero. Set the determinant equal to zero and solve for k:

(4*(-1*2) - 1*(12*2) + 2*(12*(-4+k))) = 0

Now, solve the equation for k.