Find the Determinant [[b,d,g],[h,j,k],[l,n,o]]

Problem

det(b)

Solution

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

2. Identify the minors for each element in the first row by deleting the corresponding row and column.

3. Calculate the first term by multiplying b by the determinant of the 2×2 matrix [[j,k],[n,o]]

b*(j*o−k*n)

4. Calculate the second term by multiplying −d by the determinant of the 2×2 matrix [[h,k],[l,o]]

−d*(h*o−k*l)

5. Calculate the third term by multiplying g by the determinant of the 2×2 matrix [[h,j],[l,n]]

g*(h*n−j*l)

6. Combine the terms to form the final expression for the determinant.

b*(j*o−k*n)−d*(h*o−k*l)+g*(h*n−j*l)

Final Answer

det(b)=b*(j*o−k*n)−d*(h*o−k*l)+g*(h*n−j*l)

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