Question

find the dimension of egienspace
for matrix[12
24]

Answer 1

you have a dependant matrix ...

Answer 2

it reduces to:

10
00

Answer 3

yes

Answer 4

so, you have a line, the eugene space of a line is just the 0 vector right?

Answer 5

so how to get the dimension of egienspace

Answer 6

define the eugene vectors to determine the construction of the space; then use the definition of dim

Answer 7

i got lambda =o and 5 as egienvector

Answer 8

those are values, not vectors, but its a good start

Answer 9

u mean find basis

Answer 10

yes

Answer 11

row reduce the eigene basis, and count the number of pivot points ... sounds about right to me

Answer 12

so for egien vectors i got [-2 1/2
1 1]

Answer 13

thats correct enough, ida went with

-2 1
1 2

Answer 14

now what to do

Answer 15

this defines the eigene space right?

Answer 16

how to find the dimension of it then

Answer 17

i beleive that the dim of a matrix can be defined by the number of pivot point of its rref ... does your material have a different way to define it?

Answer 18

i dont know what is pivot point

Answer 19

a pivot point can be thought of as a row reduced echelon matrix that has a leading 1 in a row

Answer 20

i got 2 pivot point
when i did row reduce

Answer 21

then if memory serves, the dimension of the eigenespace will be 2; but im trying to verify that at the moment

Answer 22

reading this to refresh my memory

http://books.google.com/books?id=QDIn6WEByGQC&pg=PA245&dq=eigenspace+dimension&hl=en&sa=X&ei=rmcCUt-nEcemygGMvICQAQ&ved=0CC0Q6AEwAA#v=onepage&q=eigenspace%20dimension&f=false

Answer 23

oy, does your material clarify any of this by chance?

Answer 24

an eigenspace is defined for each lambda:

the set of all solutions to Ax = Lx is called the eigenspace of A corresponding to L

Answer 25

the set of all the eigenvectors produces a daigonal matrix ....