Find the Determinant

Problem

det(x)

Solution

1. Set up the determinant expansion using the first column, as it contains a zero which simplifies the calculation.

2. Apply the cofactor expansion along the first column.

det(A)=x⋅det(2*x)−1⋅det(x2)+0⋅det(x2)

3. Calculate the first 2×2 determinant.

x⋅((2*x)*(2/(x3))−(2)*(−1/(x2)))

x⋅(4/(x2)+2/(x2))

x⋅(6/(x2))=6/x

4. Calculate the second 2×2 determinant.

−1⋅((x2)*(2/(x3))−(2)*(1/x))

−1⋅(2/x−2/x)

−1⋅(0)=0

5. Combine the results of the expansions to find the final value.

6/x−0=6/x

Final Answer

det(x)=6/x

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