# Differential Equations in Matrices

1. Feb 16, 2013

### 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.

2. Feb 16, 2013

### LCKurtz

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

3. Feb 16, 2013

### SteamKing

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

4. Feb 17, 2013

### Xinthose

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

5. Feb 17, 2013

### LCKurtz

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.

6. Feb 18, 2013

### 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

7. Feb 18, 2013

### D H

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

8. Feb 18, 2013

### 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