matrix-vector representation for a system

SimonChatmers

New member
Joined
Oct 16, 2015
Messages
2
I am aiming to explicitly write the matrix-vector representation of this system.
y’1 = 5y2 - y1 + y3;
y’2 = 3y1 - y2 + t2;
y’3 = y3 - ty2

This is what I have so far:
[ y’1 ] = [ -1 5 1 ] [ 0]
[ y’2 ] = [ 3 -1 0] [ t2]
[ y’3 ] = [ 0 ? 1 ] [ ? ]

Just not sure how to attack -ty2
Any help would be appreciated, thanks guys
 
Last edited:
I am aiming to explicitly write the matrix-vector representation of this system.
y’1 = 5y2 - y1 + y3;
y’2 = 3y1 - y2 + t2;
y’3 = y3 - ty2

This is what I have so far:
[ y’1 ] = [ -1 5 1 ] [ 0]
[ y’2 ] = [ 3 -1 0] [ t2]
[ y’3 ] = [ 0 ? 1 ] [ ? ]

Just not sure how to attack -ty2
Any help would be appreciated, thanks guys
What you want is
y' = A(t) y + B(t)
where y is a column matrix (vector), y' is the derivative of y, A(t) is a 3X3 matrix and B(t) is a column matrix (vector). Hopefully that is enough for your to get the following answer

HIGHLIGHT TO SEE
>>>
\(\displaystyle \begin{pmatrix}y_1'\\ y_2'\\ y_3'\end{pmatrix}=\begin{pmatrix}-1& 5& 1\\ 3& -1& 0\\ 0& -t& 1\end{pmatrix}\begin{pmatrix}y_1\\ y_2\\ y_3\end{pmatrix}+\begin{pmatrix}0\\ t^2\\ 0\end{pmatrix}\)
<<<
 
Thank you Ishuda.

Thank you Ishuda. Much appreciated

What you want is
y' = A(t) y + B(t)
where y is a column matrix (vector), y' is the derivative of y, A(t) is a 3X3 matrix and B(t) is a column matrix (vector). Hopefully that is enough for your to get the following answer

HIGHLIGHT TO SEE
>>>
\(\displaystyle \begin{pmatrix}y_1'\\ y_2'\\ y_3'\end{pmatrix}=\begin{pmatrix}-1& 5& 1\\ 3& -1& 0\\ 0& -t& 1\end{pmatrix}\begin{pmatrix}y_1\\ y_2\\ y_3\end{pmatrix}+\begin{pmatrix}0\\ t^2\\ 0\end{pmatrix}\)
<<<
 
Top