Question

write in matrix form: x'=y, y'=x+4
my teacher has not gone over this, I need help

Answer 1

what is matrix form?

Answer 2

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

Answer 3

I am working with differential equations

Answer 4

diffy qs, thats a start :)

Answer 5

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

Answer 6

does x'=Ax+b help?

Answer 7

sorry, full question:

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

Answer 8

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

Answer 9

this looks useful

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

Answer 10

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

Answer 11

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

Answer 12

idk, a vector was not mentioned

Answer 13

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

Answer 14

matrixes are vectors ...

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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