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

Problem

det(2)

Solution

1. Choose a row or column for expansion. We will use the first row to calculate the determinant.

2. Apply the cofactor expansion formula along the first row. The formula is (a_11)*(C_11)+(a_12)*(C_12)+(a_13)*(C_13)

3. Set up the 2x2 determinants for each term in the expansion.

det(A)=2*det(0)−5*det(1)+0*det(1)

4. Calculate the 2x2 determinants using the formula a*d−b*c

det(0)=(0)*(2)−(−3)*(−1)=0−3=−3

det(1)=(1)*(2)−(−3)*(2)=2+6=8

5. Substitute the values back into the expansion equation.

det(A)=2*(−3)−5*(8)+0

6. Simplify the expression to find the final result.

det(A)=−6−40=−46

Final Answer

det(2)=−46

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