anonymous
  • anonymous
let A= (4 -3 1 2 -1 1 0 0 2) a)find all eigenvalues of A. b) for each of the eigenvalues of A find the corresponding eigenspace, and give a basis for each eigenspace. ... i mostly know how to do all of this just not sure on the basis part... any help ? im pretty sure the eigenvalues are 2,2,1?
Mathematics
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anonymous
  • anonymous
let A= (4 -3 1 2 -1 1 0 0 2) a)find all eigenvalues of A. b) for each of the eigenvalues of A find the corresponding eigenspace, and give a basis for each eigenspace. ... i mostly know how to do all of this just not sure on the basis part... any help ? im pretty sure the eigenvalues are 2,2,1?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
btw A is a 3x3 matrix if you cant tell :S
anonymous
  • anonymous
hey
anonymous
  • anonymous
hello

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anonymous
  • anonymous
you familiar with paul's online notes
anonymous
  • anonymous
yep
anonymous
  • anonymous
nice
anonymous
  • anonymous
i totally agree with your comments on college
anonymous
  • anonymous
as far as paying 40 k to teach yourself, lol. ironic huh
anonymous
  • anonymous
got about 10 tabs opened up but very boring to read and im not very good at reading a bunch of boring stuff lol for that id be able to just read a textbook :S i have add...short attention span ftl
anonymous
  • anonymous
paul is boring? hes better than a text book in some sense
anonymous
  • anonymous
and yep definitely but...makes for a nice degree lol
anonymous
  • anonymous
i think the future is teaching yourself, since we're doing it anyway
anonymous
  • anonymous
as in, online supplements like khan academy and pauls notes
anonymous
  • anonymous
uhh yea idk i find it to be a bit bleh maybe more because i have... about 10 tabs of it opened that im trying to learn at once and skim through to find what i actually need to re-teach myself lol
anonymous
  • anonymous
paul is a fluttering genius. but just with calculus and linear algebra. where are is his probability notes, lol
anonymous
  • anonymous
oh cmon, he has all the examples done out
anonymous
  • anonymous
you want to do the eigenspace whachamakallit?
anonymous
  • anonymous
lol yes
anonymous
  • anonymous
alright, one sec
anonymous
  • anonymous
we’re going to start with a square matrix A and try to determine vectors x and scalars so that we will have,
anonymous
  • anonymous
scalar lambda such that A x = lamda * x
anonymous
  • anonymous
so in other words, multiplying the vector x by A is equivalent to multiplying the vector x by some scalar like 2 or 3 . remember x is a column vector, A is a square matrix, and they have to be defined
anonymous
  • anonymous
so its like multiplying A by x is lengthening the arrow of x or dilating it
anonymous
  • anonymous
x is the eigenvector, and lambda the scalar is the eigenvalue
anonymous
  • anonymous
ok for the beginning im aware you subtract lambda I from the original matrix A then you take the determinant of that and set it = to 0 to find the eigenvalues of A
anonymous
  • anonymous
yes
anonymous
  • anonymous
then you plug in each eigenvalue into the A-lambda I but then what do you do for the basis after that? the way i was taught was marked wrong on the worksheet i have
anonymous
  • anonymous
what i had done is i REF the matrix after i plugged in the eigenvalue then i took thecolumn with leading non-zero terms... the only thing i can think of is maybe i had to take that column but from the original matrix?
anonymous
  • anonymous
we did A x = lambda I * x lambda I x - A x = 0
anonymous
  • anonymous
why not RREF ?
anonymous
  • anonymous
not necessary cuz you end up with 2 -3 1 and 2 rows of 0
anonymous
  • anonymous
also not possible
anonymous
  • anonymous
well not for the eigenvalue of 2 i didnt try 1
anonymous
  • anonymous
1 you end up with 1 - 1 0 for the first row second row is 0 0 1 and then a row of 0s
anonymous
  • anonymous
i know how to find the basis of the kernal...basis of the range... but not sure on just the basis of the eigenspace lol
anonymous
  • anonymous
ok thats ok a row of zeroes is fine brb, 10 minutes
anonymous
  • anonymous
kk
anonymous
  • anonymous
kk im off to bed for the night ty anyway
anonymous
  • anonymous
ok

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