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

LetAbe a non-diagonaln-by-nmatrix of rankm. Suppose that a set of vectors, v_{1}... v_{m}, are linearly independent vectors in R^{n}such that fori= 1,...,m,

Av_{i}= 10v_{i}(v_{i}is a vector in the given set of linearly independent vectors).

(a) Prove that A is diagonalizable.

(b) Give an example of a matrix satisfying these conditions forn= 2, m = 2.

2. Relevant equations

D = S^{-1}AS

3. The attempt at a solution

I am very confused on how to do part a. I understand that one of the eigenvalue for v_{i}is 10 but I do not know what to do with that...

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# Homework Help: Prove if a Square Matrix A is Diangonalizable

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