a) Give an example showing that the determinant is not linear.
b) Give an example showing that |v|, the norm of a vector, is not linear.
My Work
A) I know that for a determinant to be linear det(ka)= k*det(a). I have a specific example that works,
B) For the norm of a vector, I have it being linear if |kv|=|k||v|. But I'm having problems finding a specific example that has |v| being not linear as I think it's not possible. Any tips or suggestions that may help me?
Try a negative value for $k$.
Also remember that linearity has a second condition, that it should split over addition, so $|v + w| = |v| + |w|$. You can find easy examples where that condition doesn't hold.