- #1

bennyska

- 112

- 0

## Homework Statement

find the diagonalizing matrix P of the matrix A

A=:

1 3 0

0 2 0

0 0 2

## Homework Equations

## 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?