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annas Group TitleBest ResponseYou've already chosen the best response.1
Let L: \[R ^{2} > R ^{2} \] be the linear transformation defined by \[L[\left(\begin{matrix}a \\ b\end{matrix}\right)]= \left[\begin{matrix}1 & 2 \\ 2 & 4\end{matrix}\right] \left(\begin{matrix}a \\ b\end{matrix}\right)\] a)find ker L b) find a set of vectors spanning range L.
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
just explain the procedure how to do it. @lalaly
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
what does ker mean
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
i guess its just L . ker is a printing mistake sorry for that uncle
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
maybe i m sure about kernel its only written ker L
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
i just need the way to solve it
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
I'm looking over my notes, I always forget this stuff
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
oh, kernel is the same thing as null space for a linear transformation i.e. the set of all \(\vec x\) in \(A\vec x=\vec 0\) is the kernel, so just solve that matrix to find part a)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
that is, solve\[ \left[\begin{matrix}1 & 2 \\ 2 & 4\end{matrix}\right] \left(\begin{matrix}a \\ b\end{matrix}\right)=0\]
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
then we'll get two eqs right ???
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
yes, from which we will get the two vectors that will make up the basis of our kernel
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
at least I think that is what they want
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
about what about part B ???
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
consulting notes again...
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
hm... I'm perhaps a bit confused because my notes don't seem to agree with wikipedia. I think the dimension of the null space, i.e. the nullity is the kernal in that case, the answer to part a) would be the number of vectors that make up the basis for the null space of your transformation matrix the answer to part b) must then be the basis itself I guess, which is the set of vectors that span \(A\vec x=\vec0\)
 2 years ago

annas Group TitleBest ResponseYou've already chosen the best response.1
ok thank you i got it :) i just need some practice now
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
yeah, me too :) welcome, good luck
 2 years ago
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