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

Problem

det(1)

Solution

1. Apply cofactor expansion along the first row to set up the determinant calculation.

1⋅det(0)−3⋅det(4)+2⋅det(4)

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

det(0)=(0)*(2)−(1)*(1)=−1

det(4)=(4)*(2)−(1)*(7)=1

det(4)=(4)*(1)−(0)*(7)=4

3. Substitute the values back into the expansion expression.

1*(−1)−3*(1)+2*(4)

4. Simplify the expression to find the final value.

−1−3+8=4

Final Answer

det(1)=4

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