Determine if the matrix can be diagonalized

blackjackmark

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Oct 20, 2006
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Sorry but can't figure out how to insert the symbols! :(
Given the matrix
3 -2 1
1 0 1
1 1 2
Determine if it can be diagonalized. If it can be, construct a matrix P and diagonalize.

First I'm calling that "matrix A", and taking
determinant of (A minus (delta times Identity matrix)) = 0
and using the charpoly program on the TI-83 which gives:
(delta^3) -(5Delta^2) + (6delta)
Factoring that gives
delta(delta^2 - 5Delta + 6) = 0
factored again gives
delta(delta-6)(delta+1)=0
which gives three values for delta:
0, 6, and -1
Plug each of those back into (A minus delta*I)
Augment that matrix with the x vector and set equal to the zero vector
for delta = 6 that gives a
vector t=
(-1)
( 1)
( 1)
For both 6 and -1 I get x=0, y=0, z=0
Which I believe means that the original vector cannot be diagonalized...but I just want to see if I've missed something.

Thanks!
 
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