Find the Determinant [[2,0,1],[2,2,4],[1,3,2]]

Problem

det(2)

Solution

1. Identify the matrix and choose a row or column for expansion. We will expand along the first row because it contains a zero.

2. Apply the cofactor expansion formula for the first row.

2⋅det(2)−0⋅det(2)+1⋅det(2)

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

det(2)=(2⋅2)−(4⋅3)=4−12=−8

det(2)=(2⋅3)−(2⋅1)=6−2=4

4. Substitute the values back into the expansion expression.

2*(−8)−0+1*(4)

5. Simplify the final arithmetic to find the determinant.

−16+4=−12

Final Answer

det(2)=−12

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