Find the Determinant [[1,2,0],[2,1,-1],[3,1,1]]

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.

1⋅det(1)−2⋅det(2)+0⋅det(2)

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

det(1)=(1)*(1)−(−1)*(1)=1+1=2

det(2)=(2)*(1)−(−1)*(3)=2+3=5

4. Substitute the values back into the expansion expression.

1*(2)−2*(5)+0

5. Simplify the final arithmetic to find the determinant.

2−10=−8

Final Answer

det(1)=−8

Want more problems? Check here!