Find the Determinant [[4,-8,-1],[9,-5,6],[8,0,14]]

Problem

det(4)

Solution

1. Choose a row or column for expansion. We will expand along the third row because it contains a zero, which simplifies the calculation.

2. Apply the cofactor expansion formula along the third row. The signs for the third row follow the pattern (+,−,+)

8*det(−8)−0*det(4)+14*det(4)

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

det(−8)=(−8)*(6)−(−1)*(−5)=−48−5=−53

det(4)=(4)*(−5)−(−8)*(9)=−20+72=52

4. Substitute the values back into the expansion expression.

8*(−53)−0+14*(52)

5. Perform the final arithmetic to find the result.

8*(−53)=−424

14*(52)=728

−424+728=304

Final Answer

det(4)=304

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