# Thread: verifying the vector...

1. ## verifying the vector...

Im supposed to verify that the vector Xp is a particular solution of the system...
Im jus not sure how...

here is the problem.

$\mathbf{X}'=\begin{pmatrix} 2 & 1\\3 &4 \end{pmatrix}\mathbf{\mathbf{X}}+\begin{pmatrix} 1 \\7 \end{pmatrix}e^{t}$

where,

$\boldsymbol{X_{p}}=\begin{pmatrix} 1\\1 \end{pmatrix}e^{t}+\begin{pmatrix} 1\\-1 \end{pmatrix}te^{t}$

maybe if i took the derivative of Xp and substituted it in? i dunno any thoughts or suggestions would be appreciated.

2. Originally Posted by slapmaxwell1
Im supposed to verify that the vector Xp is a particular solution of the system...
Im jus not sure how...

here is the problem.

$\mathbf{X}'=\begin{pmatrix} 2 & 1\\3 &4 \end{pmatrix}\mathbf{\mathbf{X}}+\begin{pmatrix} 1 \\7 \end{pmatrix}e^{t}$

where,

$\boldsymbol{X_{p}}=\begin{pmatrix} 1\\1 \end{pmatrix}e^{t}+\begin{pmatrix} 1\\-1 \end{pmatrix}te^{t}$

maybe if i took the derivative of Xp and substituted it in? i dunno any thoughts or suggestions would be appreciated.
Substitute for Xp. Substitute for X'. Simplify using basic matrix arithmetic. Show that you get equality.