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

Problem

det(3)

Solution

1. Identify the matrix and the method for calculating the determinant. We will use cofactor expansion along the first row.

2. Apply the formula for a 3×3 determinant by multiplying each element of the first row by its corresponding 2×2 minor.

3*det(4)−2*det(3)+1*det(3)

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

det(4)=(4)*(8)−(5)*(7)=32−35=−3

det(3)=(3)*(8)−(5)*(3)=24−15=9

det(3)=(3)*(7)−(4)*(3)=21−12=9

4. Substitute these values back into the expansion expression.

3*(−3)−2*(9)+1*(9)

5. Simplify the arithmetic to find the final value.

−9−18+9=−18

Final Answer

det(3)=−18

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