Find the Determinant

Problem

det(0)

Solution

1. Identify the structure of the matrix. The first column of the matrix consists entirely of zeros.

2. Apply the property of determinants regarding zero columns. If any row or column of a square matrix contains only zeros, the determinant of that matrix is zero.

3. Verify by expanding along the first column. The determinant is calculated as the sum of the elements of the first column multiplied by their respective cofactors.

0⋅(C_11)+0⋅(C_21)+0⋅(C_31)=0

Final Answer

det(0)=0

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