(adsbygoogle = window.adsbygoogle || []).push({}); Find dimension and ker of matrices ??

Let V be an F-vector space and (phi:v->v) be an F-linear transformation of V . Define what

it means for a vector v ε V to be an eigenvector of phi and what is meant by the associated

eigenvalue.

This is the form of the question during my calculations I need to calculate:

Now I have from the eigenvalues:

dim(ker()) of a matrix:

1 4 -3

0 0 0

0 0 0

and

dim(ker()) of a matrix:

1 0 -2/7

0 1 -5/7

0 0 0

Then when the I add up the the dim's I will be able to tell if it is diagonalisable.

Now in this case it is obvious, the dim(ker()) of one is 1 and another is 2. But I can't tell which one is which.

What I mean is the 1st Matrix = 2 and the second Matrix = 1 or viceversa ?

In this case in either way it will add upto 3 and as the original matrix was a 3x3 matrix it is diagonalisable right ?

In essence I don't really understand what dim or ker do ...

**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!

# Homework Help: Find dimension and ker of matrices ?

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