Find the Determinant [[5,8,6],[4,2,3],[6,0,1]]

Problem

det(5)

Solution

1. Choose a row or column for expansion. Expanding along the third row is efficient because it contains a zero.

2. Apply the cofactor expansion formula along the third row. The signs for the third row are + − +

3. Calculate the first term by multiplying the element 6 by the determinant of the 2×2 matrix remaining after removing the third row and first column.

6⋅det(8)=6*(8⋅3−6⋅2)

6*(24−12)=6*(12)=72

4. Calculate the second term involving the element 0 Since the element is zero, the entire term is zero.

−0⋅det(5)=0

5. Calculate the third term by multiplying the element 1 by the determinant of the 2×2 matrix remaining after removing the third row and third column.

1⋅det(5)=1*(5⋅2−8⋅4)

1*(10−32)=−22

6. Sum the results of the expansion to find the final determinant value.

72−0+(−22)=50

Final Answer

det(5)=50

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