Find the Determinant

Problem

det((a_11))

Solution

1. Apply the expansion formula along the first row to break the 3×3 determinant into 2×2 determinants.

2. Calculate the minors for each element in the first row by multiplying the element by the determinant of the remaining submatrix.

3. Assign alternating signs to the terms according to the pattern + − +

4. Evaluate the 2×2 determinants using the formula det(a)=a*d−b*c

5. Combine the terms to form the final algebraic expression for the determinant.

Final Answer

det((a_11))=(a_11)*((a_22)*(a_33)−(a_23)*(a_32))−(a_12)*((a_21)*(a_33)−(a_23)*(a_31))+(a_13)*((a_21)*(a_32)−(a_22)*(a_31))

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