Loser66
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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klimenkov
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If \(A=\left(\begin{matrix}e^{t} & 2e^{t} \\ 3e^{t}& 4e^{x}\end{matrix}\right)\), what is \(\frac{dA}{dt}\)?
Loser66
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\[\frac{dA}{dt}=A ~~but~~A\neq ce^tI_n\]therefore, it's false, right?
Loser66
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@MayMay_69
Loser66
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|dw:1377646939372:dw|
Loser66
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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
Loser66
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since AB=4 , BC=11. got it?
it is = 8\(\sqrt{3}\)+44\(\sqrt{3}\)=52\(\sqrt{3}\)
Loser66
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@MayMay_69 that's yours. Take it, I am gonna delete it.
Loser66
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@oldrin.bataku am I right for my own problem?
Loser66
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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
oldrin.bataku
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@Loser66 @klimenkov gave a counterexample :-p
Loser66
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that means the answer is "False" right?
oldrin.bataku
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it need not be \(A=ce^tI_n\) merely \(A=e^tB\) for constant matrix \(B\)
oldrin.bataku
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correct
Loser66
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thank you very much. @oldrin.bataku
MayMay_69
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okay thank you very very much loser
Loser66
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You got what I mean, right? @MayMay_69
MayMay_69
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yes I did thank you
Loser66
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yw