Find the Determinant [[1,2,3],[4,5,6],[5,7,9]]

Problem

det(1)

Solution

1. Set up the expansion along the first row using the cofactor method.

det(A)=1⋅det(5)−2⋅det(4)+3⋅det(4)

2. Calculate the 2×2 determinant for the first term.

5⋅9−6⋅7=45−42=3

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

4⋅9−6⋅5=36−30=6

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

4⋅7−5⋅5=28−25=3

5. Combine the results to find the final value.

1*(3)−2*(6)+3*(3)=3−12+9=0

Final Answer

det(1)=0

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