(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The matrix A has 3 distinct eigenvalues t_{1}< t_{2}< t_{3}. Let v_{i}be the unique eigenvector associated to t_{i}with a 1 as its first nonzero component. Let

D= [t_{1}0 0

0 t_{2}0

0 0 t_{3}]

and P= [v_{1}|v_{2}|v_{3}] so that the ith column of P is the eigenvector v_{i}associated to t_{i}

A=

7 2 -8

0 1 0

4 2 -5

a) Find D

b) Find P

c) Find P^{-1}

2. Relevant equations

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear Algebra Matrix Eigenvalues

**Physics Forums | Science Articles, Homework Help, Discussion**