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

Problem

det(1)

Solution

1. Identify the matrix and the method for calculating the determinant. For a 3×3 matrix, we can use cofactor expansion along any row or column.

2. Choose the third row for expansion because it contains all zeros, which simplifies the calculation significantly.

3. Apply the formula for cofactor expansion along the third row.

det(A)=(a_31)*(C_31)+(a_32)*(C_32)+(a_33)*(C_33)

4. Substitute the values from the third row into the expansion.

det(A)=0⋅(C_31)+0⋅(C_32)+0⋅(C_33)

5. Simplify the expression. Since every term is multiplied by zero, the sum is zero.

det(A)=0

Final Answer

det(1)=0

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