Find the Determinant [[2q-1,1,1],[q,1,q],[1,1,2q-1]]

Problem

det(2*q−1)

Solution

1. Set up the determinant expansion using the first row.

det(A)=(2*q−1)*det(1)−1*det(q)+1*det(q)

2. Calculate the 2×2 minor determinants.

(2*q−1)⋅(1*(2*q−1)−q(1))−1⋅(q*(2*q−1)−q(1))+1⋅(q(1)−1*(1))

3. Simplify the expressions inside the parentheses.

(2*q−1)*(2*q−1−q)−(2*q2−q−q)+(q−1)

(2*q−1)*(q−1)−(2*q2−2*q)+(q−1)

4. Expand the remaining terms.

(2*q2−2*q−q+1)−2*q2+2*q+q−1

5. Combine like terms to find the final value.

2*q2−2*q2−3*q+3*q+1−1=0

Final Answer

det(2*q−1)=0

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