Find the Determinant [[i,j,k],[175,0,100],[-14,8,-8]]

Problem

det(i)

Solution

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

2. Calculate the first minor determinant for the i component.

det(0)=(0)*(−8)−(100)*(8)=−800

3. Calculate the second minor determinant for the j component, remembering to negate it.

−det(175)=−((175)*(−8)−(100)*(−14))

−(−1400+1400)=0

4. Calculate the third minor determinant for the k component.

det(175)=(175)*(8)−(0)*(−14)=1400

5. Combine the components into the final vector expression.

Final Answer

det(i)=−800*i+1400*k

Want more problems? Check here!