(a) Consider the linear system of three firstorder

Chapter , Problem 15RP

(choose chapter or problem)

(a) Consider the linear system \(\mathbf{X}^{\prime}=\mathbf{A} \mathbf{X}\) of three first order differential equations, where the coefficien matrix is

\(\mathbf{A}=\left(\begin{array}{rrr}

5 & 3 & 3 \\

3 & 5 & 3 \\

-5 & -5 & -3

\end{array}\right)

\)

and \(\lambda=2\) is known to be an eigenvalue of multiplicity two. Find two different solutions of the system corresponding to this eigenvalue without using a special formula (such as (12) of Section 8.2).

(b) Use the procedure of part (a) to solve

\(\mathbf{X}^{\prime}=\left(\begin{array}{lll}

1 & 1 & 1 \\

1 & 1 & 1 \\

1 & 1 & 1

\end{array}\right) \mathbf{X}

\)

Text Transcription:

mathbf X^prime = mathbf A mathbf X

mathbf A = ({array} rrr 5 & 3 & 3 \\ 3 & 5 & 3 \\ -5 & -5 & -3 {array})

lambda=2

mathbf X^prime = ({array} lll 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 {array}) mathbf X