Find the Determinant [[a,s,d],[q,w,e],[z,x,c]]

Problem

det(a)

Solution

1. Identify the matrix for which the determinant needs to be calculated.

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

3. Calculate the first term by multiplying a by the determinant of the submatrix formed by removing the first row and first column.

a*det(w)=a*(w*c−e*x)

4. Calculate the second term by multiplying −s() by the determinant of the submatrix formed by removing the first row and second column.

−s*det(q)=−s*(q*c−e*z)

5. Calculate the third term by multiplying d by the determinant of the submatrix formed by removing the first row and third column.

d*det(q)=d*(q*x−w*z)

6. Combine the results of the three terms to find the final expression for the determinant.

a*(w*c−e*x)−s*(q*c−e*z)+d*(q*x−w*z)

Final Answer

det(a)=a*(w*c−e*x)−s*(q*c−e*z)+d*(q*x−w*z)

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