# Guess the eigenvalue

1. Mar 27, 2009

### fk378

1. The problem statement, all variables and given/known data
Let A be a 2x2 matrix for which there is a constant k such that the sum of the entries in each row and each column is k. Which of the following must be an eigenvector of A?

a. [1,0]
b. [0,1]
c. [1,1]

(The answer can be any or all of these)

3. The attempt at a solution
I don't know how to approach this...

Last edited: Mar 27, 2009
2. Mar 27, 2009

### tiny-tim

Hi fk378!

Sorry to say this, but … just go for the screamingly obvious :

for a 2x2 matrix ab cd, what is its effect on each of the three given vectors?

3. Mar 27, 2009

### sutupidmath

...and here i thought that eigenvalues were scalars:grumpy:

4. Mar 27, 2009

### HallsofIvy

Yes, it is. However, fk378 did ask "Which of the following must be an eigenvector of A?
Presumably, after determining which of those vectors is an eigevector, you could then determine the corresponding eigenvalue. That's certainly better than "guessing" the eigenvalue!

fk378, what is
$$\begin{bmatrix}a & b \\ c & d\end{bmatrix}\begin{bmatrix}1 \\ 0\end{bmatrix}$$?
What is
$$\begin{bmatrix}a & b \\ c & d\end{bmatrix}\begin{bmatrix}0 \\ 1\end{bmatrix}$$?
What is
$$\begin{bmatrix}a & b \\ c & d\end{bmatrix}\begin{bmatrix}1 \\ 1\end{bmatrix}$$?

Remembering, of course that a+ c= k, b+ d= k, a+ b= k, and c+ d= k.

Last edited by a moderator: Mar 27, 2009
5. Mar 27, 2009

### fk378

AH sorry! I had a typo in the subject line...it should read "guess the eigenvector"

So sorry for the confusion here.

6. Mar 27, 2009

### sutupidmath

Well, the OP defenitely edited it at some latter point, since when i looked it it read eigenvalue.

7. Mar 28, 2009

### tiny-tim

I wasn't confused