Find the Determinant [[3,1,0],[4,5,-2],[0,-1,-2]]

Problem

det(3)

Solution

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

2. Apply the cofactor expansion formula along the first row. The determinant is calculated as the sum of each element multiplied by its corresponding minor and sign.

3*det(5)−1*det(4)+0*det(4)

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

det(5)=(5)*(−2)−(−2)*(−1)=−10−2=−12

det(4)=(4)*(−2)−(−2)*(0)=−8−0=−8

4. Substitute the values back into the expansion expression.

3*(−12)−1*(−8)+0

5. Simplify the expression to find the final value.

−36+8=−28

Final Answer

det(3)=−28

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