- #1
lina29
- 85
- 0
Homework Statement
The matrix A has 3 distinct eigenvalues t1< t2< t3. Let vi be the unique eigenvector associated to ti with a 1 as its first nonzero component. Let
D= [t1 0 0
0 t2 0
0 0 t3]
and P= [v1|v2|v3] so that the ith column of P is the eigenvector vi associated to ti
A=
7 2 -8
0 1 0
4 2 -5
a) Find D
b) Find P
c) Find P-1
Homework Equations
The Attempt at a Solution
My thought to find D was to find the characteristic equation of A which I found to be (t-3)(t+1)=0 so the eigenvalues would be t=-3, t=1 I then plugged in these values into the matrix D so D became
3 0 0
0 -1 0
0 0 0
but it was counting it wrong. What did I mess up on?