Find the Determinant [[6,0,0],[-5,13,0],[9,7,4]]

Problem

det(6)

Solution

1. Identify the type of matrix provided. The matrix is a lower triangular matrix because all entries above the main diagonal are zero.

2. Apply the property for the determinant of a triangular matrix. The determinant of any triangular matrix (upper or lower) is the product of the entries on its main diagonal.

3. Multiply the diagonal elements together to find the result.

6×13×4

78×4

312

Final Answer

det(6)=312

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