The Matrix Reloaded

[Qacer]

Find a matrix P that diagonalizes


A =

[0 0 -2]
[1 2 1]
[1 0 3]

Then find the transpose of that matrix.

 

[MercenaryForHire]

Morpheus is going to kick your ass.

- M4H

 

[minus1972]

Originally posted by: MercenaryForHire
Morpheus is going to kick your ass.

- M4H

lol

 

[Qacer]

He did a pretty good job in Shaft.

 

[berger034]

Originally posted by: Qacer
He did a pretty good job in Shaft.

i like morpheus in forest gump

 

[Savarak]

Originally posted by: Qacer
Find a matrix P that diagonalizes


A =

[0 0 -2]
[1 2 1]
[1 0 3]

Then find the transpose of that matrix.

mmm, linear algebra
ok... L is Lamda

First find all of L
so
det([L 0 2]
[-1 L-2 -1]
[-1 0 L-3])

gives

(L-2)*det([L 2]
[-1 L-3])

= (L-2)(L*(L-3) + 2) = (L-2)(L^2 - 3L + 2) = (L-2)(L-1)(L-2)
= (L=2) and (L=1)

Finding the basis for Nullspace with L = 2
2 0 2 0 gives 1 0 1 0 so x -s -1
-1 0 -1 0 0 0 0 0 y = 0 = 0
-1 0 -1 0 0 0 0 0 z s 1

Finding the basis for Nullspace with L = 1
1 0 2 0 gives 1 0 2 0 so x -2s -2
-1 -1 -1 0 0 1 -1 0 y = s = 1
-1 0 -2 0 0 0 0 0 z s 1

take the basis and form a matrix P... using L=2 L=2 L=1's basis for nullspace

P= -1 -1 -2
0 0 1
1 1 1

PAP^t = D where D = 2 0 0
0 2 0
0 0 1

so

just find P^t... i'll leave that part to you

[-1 -1 -2][0 0 -2][ ] [2 0 0]
[0 0 1][1 2 1][ ] = [0 2 0]
[1 1 1][1 0 3][ ] [0 0 1]

if there are any mistakes... ignore all the above

edit: ugh, formatting came out horrible... to see it correctly, just click "quote" and read it in the message text box

 

[Marauder-]

Originally posted by: Qacer
He did a pretty good job in Shaft.

He did a better job in PeeWee's Playhouse.

 

[Ameesh]

Originally posted by: berger034

Originally posted by: Qacer
He did a pretty good job in Shaft.

i like morpheus in forest gump

hahahahah!