How would you modify Strassen's algorithm to multiply $n \times n$ matrices in which $n$ is not an exact power of 2? Show that the resulting algorithm runs in time $\Theta(n^{\lg7})$.

I'm not sure what resulting algorithm we have in mind. In any case, we can just extend it to an $n \times n$ matrix and pad it with zeroes. It's obviously $\Theta(n^{\lg7})$.