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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

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

  2. Loser66
    • 2 years ago
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    \[\frac{dA}{dt}=A ~~but~~A\neq ce^tI_n\]therefore, it's false, right?

  3. Loser66
    • 2 years ago
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    @MayMay_69

  4. Loser66
    • 2 years ago
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    |dw:1377646939372:dw|

  5. Loser66
    • 2 years ago
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    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
    • 2 years ago
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    since AB=4 , BC=11. got it? it is = 8\(\sqrt{3}\)+44\(\sqrt{3}\)=52\(\sqrt{3}\)

  7. Loser66
    • 2 years ago
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    @MayMay_69 that's yours. Take it, I am gonna delete it.

  8. Loser66
    • 2 years ago
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    @oldrin.bataku am I right for my own problem?

  9. Loser66
    • 2 years ago
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    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
    • 2 years ago
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    @Loser66 @klimenkov gave a counterexample :-p

  11. Loser66
    • 2 years ago
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    that means the answer is "False" right?

  12. oldrin.bataku
    • 2 years ago
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    it need not be \(A=ce^tI_n\) merely \(A=e^tB\) for constant matrix \(B\)

  13. oldrin.bataku
    • 2 years ago
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    correct

  14. Loser66
    • 2 years ago
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    thank you very much. @oldrin.bataku

  15. MayMay_69
    • 2 years ago
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    okay thank you very very much loser

  16. Loser66
    • 2 years ago
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    You got what I mean, right? @MayMay_69

  17. MayMay_69
    • 2 years ago
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    yes I did thank you

  18. Loser66
    • 2 years ago
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    yw

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