Find the Determinant [[a,a,b],[a,b,a],[b,a,a]]

Problem

det(a)

Solution

1. Set up the determinant calculation using cofactor expansion along the first row.

2. Expand the determinant by multiplying each element of the first row by its corresponding 2×2 minor.

a*det(b)−a*det(a)+b*det(a)

3. Calculate the 2×2 determinants using the formula a*d−b*c

a*(b*a−a2)−a*(a2−a*b)+b*(a2−b2)

4. Distribute the terms outside the parentheses.

(a2*b−a3)−(a3−a2*b)+(a2*b−b3)

5. Combine like terms to simplify the expression.

a2*b−a3−a3+a2*b+a2*b−b3

3*a2*b−2*a3−b3

Final Answer

det(a)=3*a2*b−2*a3−b3

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