Find the Eigenvalues [[3,0],[1,2]]

Problem

[[3,0],[1,2]]

Solution

1. Set up the characteristic equation by subtracting λ from the diagonal elements of the matrix A and setting the determinant of A−λ*I to zero.

det(A−λ*I)=0

2. Write the determinant for the specific 2×2 matrix.

|[3−λ,0],[1,2−λ]|=0

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

(3−λ)*(2−λ)−(0)*(1)=0

4. Simplify the equation to find the characteristic polynomial.

(3−λ)*(2−λ)=0

5. Solve for λ by setting each factor equal to zero.

3−λ=0⇒λ=3

2−λ=0⇒λ=2

Final Answer

λ=3,2

Want more problems? Check here!