The determinants for the two matrices are:

1. For problem 19, the determinant is $-78$.
2. For problem 20, the determinant is approximately $102$.

Would you like further details on how these were computed or have any questions?

Here are some related questions for practice:

1. What does the determinant tell us about a matrix's invertibility?
2. Can you explain the geometric interpretation of a 2x2 determinant?
3. How does changing a row or column in a matrix affect its determinant?
4. What happens to the determinant if two rows or columns of a matrix are identical?
5. How does the determinant help in solving systems of linear equations?

Tip: A matrix is invertible if and only if its determinant is non-zero.