Find the Determinant [[1,-4,2],[-2,8,-9],[-1,7,0]]

Problem

det(1)

Solution

1. Identify the matrix and 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 determinant is calculated as the sum of the elements in the row multiplied by their corresponding cofactors.

1⋅det(8)−(−4)⋅det(−2)+2⋅det(−2)

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

det(8)=(8)*(0)−(−9)*(7)=63

det(−2)=(−2)*(0)−(−9)*(−1)=−9

det(−2)=(−2)*(7)−(8)*(−1)=−14+8=−6

4. Substitute these values back into the expansion expression.

1*(63)+4*(−9)+2*(−6)

5. Simplify the arithmetic to find the final value.

63−36−12

63−48=15

Final Answer

det(1)=15

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