## Loser66 2 years ago If A is an n x n matrix function such that A and $$\frac{dA}{dt}$$are the same function, then A = c$$e^tI_n$$for some constant c. True or false? why? Please, help

1. klimenkov

If $$A=\left(\begin{matrix}e^{t} & 2e^{t} \\ 3e^{t}& 4e^{x}\end{matrix}\right)$$, what is $$\frac{dA}{dt}$$?

2. Loser66

$\frac{dA}{dt}=A ~~but~~A\neq ce^tI_n$therefore, it's false, right?

3. Loser66

@MayMay_69

4. Loser66

|dw:1377646939372:dw|

5. Loser66

the area of ACDE = area ABE + area BCDE = AB *EB/2 + EB*BC = 4*4$$\frac{\sqrt{3}}{2}$$+4$$\sqrt{3}$$*11

6. Loser66

since AB=4 , BC=11. got it? it is = 8$$\sqrt{3}$$+44$$\sqrt{3}$$=52$$\sqrt{3}$$

7. Loser66

@MayMay_69 that's yours. Take it, I am gonna delete it.

8. Loser66

@oldrin.bataku am I right for my own problem?

9. Loser66

I am sorry for messing up. May may asked for help but he/she has no link, I used my post to anser him/her

10. oldrin.bataku

@Loser66 @klimenkov gave a counterexample :-p

11. Loser66

that means the answer is "False" right?

12. oldrin.bataku

it need not be $$A=ce^tI_n$$ merely $$A=e^tB$$ for constant matrix $$B$$

13. oldrin.bataku

correct

14. Loser66

thank you very much. @oldrin.bataku

15. MayMay_69

okay thank you very very much loser

16. Loser66

You got what I mean, right? @MayMay_69

17. MayMay_69

yes I did thank you

18. Loser66

yw