Find the Determinant [[0,2,2],[-1,6,-2],[6,2.2,8]]

Problem

det(0)

Solution

1. Identify the matrix and choose a row or column for expansion. Expanding along the first row is efficient because it contains a zero.

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

0⋅det(6)−2⋅det(−1)+2⋅det(−1)

3. Calculate the 2×2 determinant for the second term.

det(−1)=(−1)*(8)−(−2)*(6)

−8+12=4

4. Calculate the 2×2 determinant for the third term.

det(−1)=(−1)*(2.2)−(6)*(6)

−2.2−36=−38.2

5. Substitute the values back into the expansion expression.

0−2*(4)+2*(−38.2)

6. Simplify the final arithmetic.

−8−76.4=−84.4

Final Answer

det(0)=−84.4

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