Find the Determinant [[4,2,8],[-2,1,-4],[3,1,6]]

Problem

det(4)

Solution

1. Identify the matrix and choose a row or column for expansion. We will use the first row to calculate the determinant.

2. Apply the cofactor expansion formula for a 3×3 matrix.

4*det(1)−2*det(−2)+8*det(−2)

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

det(1)=(1)*(6)−(−4)*(1)=6+4=10

det(−2)=(−2)*(6)−(−4)*(3)=−12+12=0

det(−2)=(−2)*(1)−(1)*(3)=−2−3=−5

4. Substitute the values back into the expansion expression.

4*(10)−2*(0)+8*(−5)

5. Simplify the arithmetic to find the final value.

40−0−40=0

Final Answer

det(4)=0

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