Answer:
k ≠ -14/3
Step-by-step explanation:
A square matrix is invertible if and only if its determinant is not zero.
Determinant
The determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:
det = (6)(k) -(-7)(4) = 6k +28
Restriction on k
The requirement that the determinant is not zero places a restriction on k.
6k +28 ≠ 0
k +14/3 ≠ 0 . . . . . . divide by 6
k ≠ -14/3 . . . . . . . . subtract 14/3
For the matrix to be invertible, the value of k must not be -14/3.
