Find the Determinant [[1,2,3],[4,5,6],[7,8,0]]

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*(0)−6*(8)=−48

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

4*(0)−6*(7)=−42

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

4*(8)−5*(7)=32−35=−3

5. Combine the results by multiplying by the row elements and summing them.

1*(−48)−2*(−42)+3*(−3)

6. Simplify the arithmetic to find the final value.

−48+84−9=27

Final Answer

det(1)=27

Want more problems? Check here!