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

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 cofactor.

0⋅det(−4)−(−1)⋅det(3)+4⋅det(3)

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

det(3)=(3)*(3)−(1)*(1)=8

det(3)=(3)*(−2)−(−4)*(1)=−6+4=−2

4. Substitute the values back into the expansion expression.

0*(…)+1*(8)+4*(−2)

5. Simplify the arithmetic to find the final value.

8−8=0

Final Answer

det(0)=0

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