Find the Determinant [[2,4,0],[-3,1,-7],[1,1,1]]

Problem

det(2)

Solution

1. Identify the matrix and choose a row or column for expansion. We will expand along the first row because it contains a zero.

2. Apply the formula for the determinant of a 3×3 matrix using the entries of the first row: (a_11) (a_12) and (a_13)

3. Calculate the first term by multiplying (a_11) by the determinant of its 2×2 minor.

2⋅det(1)=2*(1*(1)−(−7)*(1))

2*(1+7)=16

4. Calculate the second term by multiplying −(a_12) by the determinant of its 2×2 minor.

−4⋅det(−3)=−4*((−3)*(1)−(−7)*(1))

−4*(−3+7)=−16

5. Calculate the third term by multiplying (a_13) by the determinant of its 2×2 minor.

0⋅det(−3)=0

6. Sum the results of the three terms to find the final determinant.

16−16+0=0

Final Answer

det(2)=0

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