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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.

Learn how to evaluate the determinants of two 3x3 matrices with a detailed solution. This problem covers key concepts in linear algebra, including the formula for computing the determinant of a 3x3 matrix. Suitable for students in Grades 11-12 or early college.

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