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

Problem

det(1)

Solution

1. Identify the matrix and choose a row or column for expansion. We will use the first row to calculate the determinant.

2. Apply the cofactor expansion formula along the first row.

1⋅det(1)−1⋅det(0)+0⋅det(0)

3. Calculate the 2×2 determinants using the formula det(a)=a*d−b*c

det(1)=(1)*(−1)−(−1)*(0)=−1

det(0)=(0)*(−1)−(−1)*(−1)=−1

4. Substitute the values back into the expansion expression.

1*(−1)−1*(−1)+0

5. Simplify the arithmetic to find the final value.

−1+1=0

Final Answer

det(1)=0

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