Find the Determinant [[10,-1,5],[6,-2,4],[1,-3,1]]

Problem

det(10)

Solution

1. Apply the expansion formula along the first row to break the 3×3 determinant into 2×2 determinants.

10*det(−2)−(−1)*det(6)+5*det(6)

2. Calculate the 2×2 determinants using the formula det(a)=a*d−b*c

det(−2)=(−2)*(1)−(4)*(−3)=−2+12=10

det(6)=(6)*(1)−(4)*(1)=6−4=2

det(6)=(6)*(−3)−(−2)*(1)=−18+2=−16

3. Substitute the values back into the expansion expression.

10*(10)+1*(2)+5*(−16)

4. Simplify the expression to find the final scalar value.

100+2−80

102−80=22

Final Answer

det(10)=22

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