Question

In: Advanced Math

find the general solution of the following as follows Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2...

find the general solution of the following as follows
Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2

a) find the 2x2 matrix that satisfies Yn+1=AYn
b) Find the characteristic value of A and its corresponding characteristic vector
c) express X0 = (1 2)as a linear combination of characteristic vector
d) find Yn
e) find Xn

Expert Solution

Solution:

(a) In matrix form we can write the equation as

where .

(b) The characteristic values of the coefficient matrix A are given by

To find the characteristic vector corresponding to , we need to solve

is a characteristic vector corresponding to the characteristic value .

To find the characteristic vector corresponding to , we need to solve

is a characteristic vector corresponding to the characteristic value

(c) Now we have given that

Let

(d) Hence \

(e) Hence

Colby Messinger answered 2 years ago

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