Quick diagonalize matrix (row reduce)

[Nope]

quick please..diagonalize matrix (row reduce)

Homework Statement

http://www.math4all.in/public_html/linear algebra/chapter10.1.html
10.1.5 Examples: (ii)
this part:

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are both eigenvector for the eigenvalue λ = 3. Similarly, for λ = 6, since
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Does it matter if I reduce it to rref?

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

http://www.math4all.in/public_html/linear algebra/chapter10.1.html
10.1.5 Examples: (ii)
this part:

-----------------------------------------------------------------------------------------

are both eigenvector for the eigenvalue λ = 3. Similarly, for λ = 6, since
-----------------------------------------------------------------------------------------

Does it matter if I reduce it to rref?

Your question doesn't make much sense. The matrices you show are NOT eigenvectors. In the link you gave, it shows two vectors that are the eigenvectors for the eigenvalue 3.

What do you mean by "reduce it to rref"?

 

[Nope]

oh i I figure it out...
I was just asking
Do I get the same eigenvector (which is 0,1,1) if I
transform
-3,0,0
0,1,-1
0,0,0
to rref

In reduced row-echelon form (RREF), the matrix above is
1 0 0
0 1 -1
0 0 0

The only thing that changed is row 1.
You'll get exactly the same eigenvector from this matrix as from the unreduced one.

 

[Nope]

And using this calculator
http://wims.unice.fr/wims/en_tool~linear~matrix.html
I found that
Value Multiplicity Vector
6 1 (0,1,1)
3 2 (1,0,1), (0,1,-1/2)

(1,0,1) and (0,1,1) is right, but (0,1,-1/2) is different to the website , which is (1/2,1,0)
I m confused..

 

[Mark44]

And using this calculator
http://wims.unice.fr/wims/en_tool~linear~matrix.html
I found that
Value Multiplicity Vector
6 1 (0,1,1)
3 2 (1,0,1), (0,1,-1/2)

(1,0,1) and (0,1,1) is right, but (0,1,-1/2) is different to the website , which is (1/2,1,0)
I m confused..

It's easy to check. Substitute each of these two vectors (i.e., <0, 1, -1/2> and <1/2, 1, 0> in the equation Ax = 3x. If they both make a true statement, they're both eigenvectors.