Find the Determinant [[2,-5,7],[0,-8,1],[3,-2,-1]]

Problem

det(2)

Solution

1. Set up the expansion along the first column to take advantage of the zero.

2. Calculate the first minor by multiplying the element 2 by the determinant of the 2×2 matrix remaining after removing the first row and first column.

2⋅det(−8)=2*((−8)*(−1)−(1)*(−2))

2*(8+2)=20

3. Calculate the second minor, which is multiplied by 0 so it contributes nothing to the total.

−0⋅det(−5)=0

4. Calculate the third minor by multiplying the element 3 by the determinant of the 2×2 matrix remaining after removing the third row and first column.

3⋅det(−5)=3*((−5)*(1)−(7)*(−8))

3*(−5+56)=3*(51)=153

5. Sum the results of the cofactor expansion to find the final determinant.

20−0+153=173

Final Answer

det(2)=173

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