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

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 the 2×2 matrix remaining after removing the first row and first column.

3⋅det(3)=3*(3⋅6−5⋅(−1))

3*(18+5)=3*(23)=69

3. Calculate the second term by multiplying the element (a_12)=−1 by −1 and the determinant of the 2×2 matrix remaining after removing the first row and second column.

−(−1)⋅det(6)=1*(6⋅6−5⋅2)

1*(36−10)=26

4. Calculate the third term by multiplying the element (a_13)=4 by the determinant of the 2×2 matrix remaining after removing the first row and third column.

4⋅det(6)=4*(6⋅(−1)−3⋅2)

4*(−6−6)=4*(−12)=−48

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

69+26−48=47

Final Answer

det(3)=47

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