(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?

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# Homework Help: Linear Algebra Matrix Eigenvalues

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