Final answer:
The value of c for which the matrix is non-invertible, or singular, is 0. The determinant of the matrix is zero when c is 0, indicating that it cannot be inverted.
Step-by-step explanation:
To determine the value of c which makes the matrix non-invertible, we need to find when the matrix has a determinant of zero. A matrix is non-invertible or singular if its determinant is zero. For the given matrix:
| 3 2 -1 |
| 1 0 2 |
|-2 -2 c |
the determinant is:
3(0*c - 2*(-2)) - 2(1*c - 2*(-2)) - 1(1*(-2) - 0*(-2))
= 3(2) - 2(c + 4) + 2
= 6 - 2c - 8 + 2
= 0 - 2c
Setting this equal to zero gives us the equation:
0 - 2c = 0
Solving this for c we find that c must be equal to 0.
Therefore, the value of c which makes this matrix non-invertible is 0.