Find the Eigenvalues [[0,1],[2 square root of a,0]]

Problem

[[0,1],[2√(,a),0]]

Solution

1. Identify the matrix A and the characteristic equation formula det(A−λ*I)=0 where λ represents the eigenvalues.

A=[[0,1],[2√(,a),0]]

2. Set up the characteristic equation by subtracting λ from the diagonal elements and calculating the determinant.

det(−λ)=0

3. Calculate the determinant by multiplying the diagonal elements and subtracting the product of the off-diagonal elements.

(−λ)*(−λ)−(1)*(2√(,a))=0

4. Simplify the resulting quadratic equation.

λ2−2√(,a)=0

5. Solve for λ by isolating the variable and taking the square root of both sides.

λ2=2√(,a)

λ=±√(,2√(,a))

Final Answer

λ=±√(,2√(,a))

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