Intersection of the NullT and ImT - Mathematics Stack Exchange
2015年2月11日 · $\begingroup$ What do you ask is "the correct answer"? You have shown nothing but unproved things. You wrote $\;\dim\ker T=0\;$, which of course is false in the general case (but this doesn't matter that much: you can't write without a proof such a thing and seriously expect things will go smoothly in an university level exam), and from here you deduce false …
linear algebra - if $T: V\to V$ and $ dim(KerT)+dim(ImT)=dimV
2023年3月29日 · (mean V Direct sum of KerT and ImT ) not matter the basis i am using? i know that Linear Transformation its not affected by basis we use but when i am using matrix it is Lean on the basis, so i am little confused. if i trying to proof that V is Direct sum of KerT and ImT
Find a base for $ImT$ using the Transformation matrix
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Find a basis for KerT and ImT (T is a linear transformation)
2019年6月15日 · $\begingroup$ You can, for instance, use the "dimensions. thm", and you have that $5=\dim(Ker) + \dim(Im)$ , so you know which is the dimension of the kernel.
V = ImT \oplus \ KerT - Mathematics Stack Exchange
I'm trying to prove the following: $\ \ \ Im L \oplus KerL = V \ \ $ when $\ \ \ L = T^k \ \ \ $ When: $\mathbb T: V \rightarrow V \ $ and $ ImT \oplus KerT =V$ My take on this is below. I would like to know if my proof is a proper one? If not can you point me to where it fails? Any comment's and suggestions would be much appreciated
Find Base for ImT and KerT - Mathematics Stack Exchange
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Does $V=im(T)\oplus ker(T)$ hold if $T$ is an idempotent linear ...
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linear algebra - Proof that columns of an invertible matrix are ...
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integration - Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2 ...
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Methods for choosing $u$ and $dv$ when integrating by parts?
2017年2月1日 · $\begingroup$ Well, this sorta works. Except it really only works with a small subset of functions. Complexity is really hard to define in general.