Find the Determinant [[0.25,1,1],[4,3,-5],[-1,-3,-4]]

Problem

det(0.25)

Solution

1. Apply the cofactor expansion along the first row to set up the calculation for the 3×3 determinant.

D=0.25*det(3)−1*det(4)+1*det(4)

2. Calculate the 2×2 minor for the first term using the formula a*d−b*c

det(3)=(3)*(−4)−(−5)*(−3)=−12−15=−27

3. Calculate the 2×2 minor for the second term.

det(4)=(4)*(−4)−(−5)*(−1)=−16−5=−21

4. Calculate the 2×2 minor for the third term.

det(4)=(4)*(−3)−(3)*(−1)=−12+3=−9

5. Substitute the minor values back into the expansion equation.

D=0.25*(−27)−1*(−21)+1*(−9)

6. Simplify the expression by performing the arithmetic operations.

D=−6.75+21−9

D=5.25

Final Answer

det(0.25)=5.25

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