Find the Characteristic Equation [[0.66-0.01,-0.73],[0.1,-0.1-0.01]]

Problem

det([[0.66−0.01,−0.73],[0.1,−0.1−0.01]]−λ*I)=0

Solution

1. Simplify the entries of the matrix by performing the subtractions within the brackets.

A=[[0.65,−0.73],[0.1,−0.11]]

2. Set up the characteristic equation by subtracting λ from the diagonal elements and setting the determinant of the resulting matrix to zero.

det(0.65−λ)=0

3. Apply the determinant formula for a 2×2 matrix, which is (a*d−b*c)

(0.65−λ)*(−0.11−λ)−(−0.73)*(0.1)=0

4. Expand the product of the binomials using the FOIL method.

λ2−0.65*λ+0.11*λ−0.0715+0.073=0

5. Combine like terms to reach the final quadratic form of the characteristic equation.

λ2−0.54*λ+0.0015=0

Final Answer

λ2−0.54*λ+0.0015=0

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