Find the Determinant [[1,1,1],[0,0,1],[0,1,0]]

Problem

det(1)

Solution

1. Identify the matrix and choose a row or column for expansion. Expanding along the first column is efficient because it contains two zeros.

2. Apply the cofactor expansion formula along the first column. The determinant is the sum of the elements in the column multiplied by their corresponding cofactors.

3. Calculate the determinant using the first element of the first column.

det(A)=1⋅det(0)−0⋅det(1)+0⋅det(1)

4. Simplify the expression by evaluating the 2×2 determinant.

det(0)=(0⋅0)−(1⋅1)

5. Compute the final numerical value.

det(A)=1⋅(0−1)

det(A)=−1

Final Answer

det(1)=−1

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