Brandie Group Title write in matrix form: x'=y, y'=x+4 my teacher has not gone over this, I need help 2 years ago 2 years ago

1. amistre64 Group Title

what is matrix form?

2. amistre64 Group Title

some sort of subject that this pertains to would help out as well

3. Brandie Group Title

I am working with differential equations

4. amistre64 Group Title

diffy qs, thats a start :)

5. amistre64 Group Title

and is this the start of a problem or like midways thru?

6. Brandie Group Title

does x'=Ax+b help?

7. Brandie Group Title

sorry, full question: write each system of differential equations in matrix form, i.e. x'=Ax+b

8. amistre64 Group Title

let me look that up to see if im familiar with it by another name ...

9. amistre64 Group Title

this looks useful http://tutorial.math.lamar.edu/Classes/DE/SystemsDE.aspx

10. Brandie Group Title

yeah, its actually helping me on other questions, but not this one. But thanks. :)

11. amistre64 Group Title

is your vector [x',y'] by chance?

12. Brandie Group Title

idk, a vector was not mentioned

13. amistre64 Group Title

x'=0x+y+0 y'=x+0y+4 $\binom{x'}{y'}=\begin{pmatrix}0&1&0\\1&0&4 \end{pmatrix}\binom{x}{y}$ maybe

14. amistre64 Group Title

matrixes are vectors ...

15. amistre64 Group Title

$\binom{x'}{y'}=\begin{pmatrix}0&1\\1&0 \end{pmatrix}\binom{x}{y}+\binom{0}{4}$ maybe

16. Mr.Math Group Title

We have the system $$x'=0x+y$$ $$y'=x+0y+4$$. We can write this as: $${x' \choose y'}=\left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]{x\choose y}+{0\choose 4}.$$

17. amistre64 Group Title

yay!! thats good enough for validation to me :)

18. Brandie Group Title

really? i thought it was more involved than that, cool. Thanks guys!

19. Mr.Math Group Title

Although I think it can be solved without finding any eigenvalues or eigenvectors.