Find the Determinant [[2,-4,6],[1,4,0],[-1,2,4]]

Problem

det(2)

Solution

1. Choose a row or column for expansion. We will expand along the first row using the cofactor expansion method.

2. Set up the expansion by multiplying each element of the first row by its corresponding minor and alternating signs.

det(A)=2*det(4)−(−4)*det(1)+6*det(1)

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

det(4)=(4)*(4)−(0)*(2)=16

det(1)=(1)*(4)−(0)*(−1)=4

det(1)=(1)*(2)−(4)*(−1)=2+4=6

4. Substitute the values back into the expansion expression.

det(A)=2*(16)+4*(4)+6*(6)

5. Simplify the expression to find the final result.

det(A)=32+16+36=84

Final Answer

det(2)=84

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