Find the Characteristic Equation [[0.2,0.3],[0.8,0.7]]

Problem

[[0.2,0.3],[0.8,0.7]]

Solution

1. Identify the matrix A and the formula for the characteristic equation, which is given by det(A−λ*I)=0

2. Subtract λ from the diagonal elements of the matrix to form the matrix A−λ*I

A−λ*I=[[0.2−λ,0.3],[0.8,0.7−λ]]

3. Calculate the determinant of the resulting 2×2 matrix by finding the product of the diagonal elements minus the product of the off-diagonal elements.

det(A−λ*I)=(0.2−λ)*(0.7−λ)−(0.3)*(0.8)

4. Expand the algebraic expression using the FOIL method.

(0.2−λ)*(0.7−λ)=0.14−0.2*λ−0.7*λ+λ2

λ2−0.9*λ+0.14

5. Subtract the product of the off-diagonal elements, which is 0.24

λ2−0.9*λ+0.14−0.24

6. Simplify the expression to obtain the final polynomial.

λ2−0.9*λ−0.1

Final Answer

det([[0.2,0.3],[0.8,0.7]]−λ*I)=λ2−0.9*λ−0.1=0

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