3.Find the basis of eigen vectors and diaganalize of the matrix
-8 11 3
4 -1 3
-4 10 6

Question

3.Find the basis of eigen vectors and diaganalize of the matrix   
-8    11    3
  4    -1    3
-4   10     6

anonymous · Answer

are the vectors linear independent?

anonymous · Answer

Well If you don't know if the vectors are lin indepent by inspection then row reduce to echelon form.

anonymous · Answer

Then determine the number of pivot columns.

anonymous · Answer

this is a step by step tutorial http://www.jtaylor1142001.net/calcjat/Solutions/Matrix/Eigenvalues/Eigenvalues-3x3-Constants/EV-3x3-Const-Layers.htm

anonymous · Answer

what matrix are u talking about?

anonymous · Answer

We can still find the eigenvectors but we still have to determine what the basis is and that's the easy part of this problem so let's do that first.

anonymous · Answer

The tutorial only finds the eigenvalues and does not find the eigenvectors or even diaganalizes the matrix at all.

anonymous · Answer

How much have yo done?

anonymous · Answer

to get eigen vectors u jus need to sub in the eigen values lol... anyway thread closed

anonymous · Answer

you reduced matrix
then solution equation Ax=0
A is matrix
x is basis of eigen vectors

anonymous · Answer

@chanh_chung So in order to get the basis of the matrix you still need to have n vectors. I thought all you have to do is get rid of all the lin dependent columns from the matrix.

anonymous · Answer

reduced matrix I all you have to do is get rid of all the lin dependent row from the matrix.

anonymous · Answer

You don't take away row because if you do then you lose span. The key point about Basis is that it must span the vector space and have a set of lin ind vectors. When we refer to span we refer to the entries the matrix. The basis must span R^m which is this case is n=3

this means that the vectors in the basis must have three entries but if you take away a row you take away an entry therefor it doesn't span R^3 and we conclude that it is not a basis.

anonymous · Answer

Dude no one is going to give you the answer.

anonymous · Answer

I think rows or columns is the same

anonymous · Answer

Nope they are not the same.

anonymous · Answer

my vector is x=(1,-1,1)

anonymous · Answer

Nope you need to have two vectors for the basis.

anonymous · Answer

and I think your method also true
your vector are???????

anonymous · Answer

They are all lin dependent on each other so it doesn't matter what vector you take out to form the basis.

anonymous · Answer

I don't you study how 
as far as I know the both the same.