Find the Determinant [[3,1,2],[5,3,-6],[2,4,3]]

Problem

det(3)

Solution

1. Apply the expansion formula for a 3×3 determinant along the first row.

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

3⋅det(3)=3*(3⋅3−(−6)⋅4)

3*(9+24)=3*(33)=99

3. Calculate the second term by multiplying the element (a_12)=1 by the determinant of its 2×2 minor and applying a negative sign.

−1⋅det(5)=−1*(5⋅3−(−6)⋅2)

−1*(15+12)=−1*(27)=−27

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

2⋅det(5)=2*(5⋅4−3⋅2)

2*(20−6)=2*(14)=28

5. Sum the results of the three terms to find the final determinant value.

99−27+28=100

Final Answer

det(3)=100

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