Find the Determinant [[1,2,5],[4,5,6],[1,2,8]]

Problem

det(1)

Solution

1. Identify the matrix and choose a row or column for expansion. We will use the first row to perform cofactor expansion.

2. Apply the formula for the determinant of a 3×3 matrix by multiplying each element of the first row by its corresponding 2×2 minor.

1⋅det(5)−2⋅det(4)+5⋅det(4)

3. Calculate the 2×2 determinants using the formula a*d−b*c

det(5)=(5⋅8)−(6⋅2)=40−12=28

det(4)=(4⋅8)−(6⋅1)=32−6=26

det(4)=(4⋅2)−(5⋅1)=8−5=3

4. Substitute these values back into the expansion expression.

1*(28)−2*(26)+5*(3)

5. Simplify the arithmetic to find the final result.

28−52+15=−9

Final Answer

det(1)=−9

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