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The determinant of the matrix \( A \) is \( \det(A) = 3516 \).

Would you like further details or clarification on this? Here are 5 related questions to explore:

1. How can determinants be used to solve systems of linear equations?
2. What is the geometric interpretation of a determinant for a 2x2 or 3x3 matrix?
3. How does the determinant change when performing row operations on a matrix?
4. How is the cofactor expansion method applied to find a matrix determinant?
5. What properties of a matrix can we infer from its determinant?

**Tip:** A matrix with a determinant of zero is singular, meaning it doesn't have an inverse.

Calculate the determinant of the matrix A:
A = [ [0, 12, 4, 8], [0, 2, 3, 9], [-3, -9, -2, -5], [0, -11, 11, -1] ]

Learn how to find the determinant of a 4x4 matrix. This problem involves key concepts in linear algebra, including matrix determinants, cofactor expansion, and the properties of determinants. Suitable for students in Grades 10-12.

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