Find the Determinant (-2)[[340,2,2],[435,1,4],[225,1,1]]

Problem

−2*|[340,2,2],[435,1,4],[225,1,1]|

Solution

1. Identify the scalar and the matrix. We need to calculate the determinant of the 3×3 matrix and then multiply the result by −2

2. Expand the determinant along the first row using the cofactor expansion method.

det(=)*340*|[1,4],[1,1]|−2*|[435,4],[225,1]|+2*|[435,1],[225,1]|

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

|[1,4],[1,1]|=(1)*(1)−(4)*(1)=−3

|[435,4],[225,1]|=(435)*(1)−(4)*(225)=435−900=−465

|[435,1],[225,1]|=(435)*(1)−(1)*(225)=435−225=210

4. Substitute these values back into the expansion of the 3×3 determinant.

det(=)*340*(−3)−2*(−465)+2*(210)

det(=)−1020+930+420

det(=)*330

5. Multiply the resulting determinant by the scalar −2

−2×330=−660

Final Answer

−2*|[340,2,2],[435,1,4],[225,1,1]|=−660

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