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.

2. Calculate the first term by multiplying x by the determinant of the 2×2 matrix remaining after removing the first row and first column.

x⋅det(x)=x*(x2−1/25)

3. Calculate the second term by multiplying −(−1/5) by the determinant of the 2×2 matrix remaining after removing the first row and second column.

1/5⋅det(−1/5)=1/5*(−x/5−1/25)

4. Calculate the third term by multiplying −1/5 by the determinant of the 2×2 matrix remaining after removing the first row and third column.

−1/5⋅det(−1/5)=−1/5*(1/25+x/5)

5. Combine and simplify all the terms to find the final polynomial expression.

x3−x/25−x/25−1/125−1/125−x/25

6. Group like terms to reach the simplified form.

x3−3*x/25−2/125

Final Answer

det(x)=x3−3/25*x−2/125

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