Find the Determinant

Problem

det(8)

Solution

1. Set up the determinant calculation using cofactor expansion along the second row to take advantage of the zero.

2. Apply the cofactor expansion formula for the second row.

det(A)=−8*x*det(√(8,5))+4*det(8)−0*det(8)

3. Calculate the 2×2 determinant for the first term.

det(√(8,5))=7√(8,5)−72

4. Calculate the 2×2 determinant for the second term.

det(8)=(8)*(7)−(9)*(6)=56−54=2

5. Substitute these values back into the expansion expression.

det(A)=−8*x*(7√(8,5)−72)+4*(2)

6. Distribute the terms to simplify the expression.

det(A)=−56*x√(8,5)+576*x+8

Final Answer

det(8)=−56*x√(8,5)+576*x+8

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