Find the Determinant [[10,11,12],[13,14,15],[16,17,10]]

Problem

det(10)

Solution

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

det(A)=10*det(14)−11*det(13)+12*det(13)

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

det(14)=(14)*(10)−(15)*(17)=140−255=−115

det(13)=(13)*(10)−(15)*(16)=130−240=−110

det(13)=(13)*(17)−(14)*(16)=221−224=−3

3. Substitute the values back into the expansion expression.

det(A)=10*(−115)−11*(−110)+12*(−3)

4. Simplify the expression by performing the multiplications and additions.

det(A)=−1150+1210−36

det(A)=60−36

det(A)=24

Final Answer

det(10)=24

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