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

Problem

det(3)

Solution

1. Choose a row or column for expansion. We will expand along the first row using the formula for a 3×3 determinant.

2. Set up the expansion by multiplying each element of the first row by its corresponding 2×2 minor and applying the alternating signs (+,−,+)

3*det(1)−2*det(0)+(−1)*det(0)

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

det(1)=(1)*(1)−(5)*(0)=1

det(0)=(0)*(1)−(5)*(2)=−10

det(0)=(0)*(0)−(1)*(2)=−2

4. Substitute the values back into the expansion expression.

3*(1)−2*(−10)−1*(−2)

5. Simplify the expression to find the final value.

3+20+2=25

Final Answer

det(3)=25

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