Find the Determinant

Problem

det(x)

Solution

1. Apply the cofactor expansion along the first row to set up the calculation for the 3×3 determinant.

x*det(x)−(−1/6)*det(−1/6)+(−1/6)*det(−1/6)

2. Calculate the 2×2 determinants using the formula a*d−b*c for each term.

x*(x2−1/36)+1/6*(−x/6−1/36)−1/6*(1/36+x/6)

3. Distribute the terms to expand the expression into a polynomial.

x3−x/36−x/36−1/216−1/216−x/36

4. Combine like terms by grouping the x terms and the constant terms.

x3−3*x/36−2/216

5. Simplify the fractions to reach the final polynomial form.

x3−x/12−1/108

Final Answer

det(x)=x3−1/12*x−1/108

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