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

find the diagonalizing matrix P of the matrix A

A=:

1 3 0

0 2 0

0 0 2

2. Relevant equations

3. The attempt at a solution

so i do the whole A-[tex]\lambda[/tex]I_{3}thing and i find my eigenvalues to be [tex]\lambda = 1, 2[/tex]

when i do [tex]\lambda[/tex] = 1, i get the matrix

0 3 0

0 1 0

0 0 1

which turns into

0 1 0

0 0 1

0 0 0

i guess here's my main question. can i have any eigenvectors from here that satisfy this equation? i'm getting a different solution than the book, but it's been a while since i've taken linear algebra (this is a differential equations class and this parts review), and i seem to recall that this doesn't need to be like the book (i.e. the book presents one possible solution; as long as my solution is linearly independent, it should be valid).

...

okay, so i just plugged it in and found out i'm incorrect.

so how do i find the solution to

0 1 0 | 0

0 0 1 | 0

0 0 0 | 0?

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# Homework Help: Eigenvectors of a 3x3 matrix (specifically diagonalizing), but need a clarifying hint

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