Differential Equations in Matrices

[Xinthose]

I realize that Δ(s) is the cross product of the matrix on the left, but how did the solutions manual get the matrix on the far right multiplied by R_1(s) and R_2(s)? I need those matrix values to do the rest of the problem. Any help is appreciated, thank you.

 

[LCKurtz]

I realize that Δ(s) is the cross product of the matrix on the left, but how did the solutions manual get the matrix on the far right multiplied by R_1(s) and R_2(s)? I need those matrix values to do the rest of the problem. Any help is appreciated, thank you.

They multiplied both sides of the first equation by the inverse of the matrix on the left to solve for $Y_1(s)$ and $Y_2(s)$.

 

[SteamKing]

I think Delta (s) is technically the determinant of the left most s matrix, rather than the cross product.

 

[Xinthose]

I still don't see how they did it, sorry.

 

[LCKurtz]

I still don't see how they did it, sorry.

Do you know how to find the inverse of$$
\begin{bmatrix}
s(s+2) & 3\\
3s+1 & s^2-1

\end{bmatrix}$$If so, do that first. Then multiply it on the left of$$
\begin{bmatrix}
1 & 1\\
s & 1
\end{bmatrix}$$and see if that helps you.

 

[Xinthose]

yup, thank you LCKurtz. That was the obvious answer. Now that I have a TI-nspire CAS, I can just type it in and it comes out

 

[D H]

You don't need a calculator for this. Sometimes a calculator hinders learning.

 

[Xinthose]

True, but that new CAS is awesome. I did the math by hand eventually, after many, many google searches on the right steps to take