Find the Determinant [[0,4,6],[3,5,4],[6,8,6]]

Problem

det(0)

Solution

1. Set up the expansion along the first row to calculate the determinant of the 3×3 matrix.

2. Apply the formula for the determinant by multiplying each element of the first row by its corresponding 2×2 minor and alternating signs.

D=0⋅det(5)−4⋅det(3)+6⋅det(3)

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

det(3)=(3⋅6)−(4⋅6)=18−24=−6

det(3)=(3⋅8)−(5⋅6)=24−30=−6

4. Substitute these values back into the main expression.

D=0−4*(−6)+6*(−6)

5. Simplify the arithmetic to find the final result.

D=24−36=−12

Final Answer

det(0)=−12

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