Search for question
Question

Each of the vector functions x1, x2, x3 is a solution to the linear system of DE's.Determine whether they form a fundamental set of solutions for that system.If they do,

what is the general solution to the system? x_{1}=\left[\begin{array}{l} e^{2 t} \\ e^{2 t} \\ e^{2 t} \end{array}\right] \quad x_{2}=\left[\begin{array}{c} -e^{-t} \\ 0 \\ e^{-t} \end{array}\right] \quad x_{3}=\left[\begin{array}{c} 0 \\ e^{-t} \\ -e^{-t} \end{array}\right] x^{\prime}=\left[\begin{array}{lll} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}\right] x

Fig: 1

Fig: 2

Fig: 3