Understanding the Eigenvalue Problem for a 4x4 Matrix with Rank 1 and Trace 10

[Nexttime35]

Homework Statement

Let there be a 4X4 Matrix A with dim(im(A), or rank = 1 , and trace=10. What are the Eigenvalues of A? Are there any multiplicities?

The Attempt at a Solution

While I understand that the trace of a matrix that's 4X4 = the sum of the diagonal elements, I'm confused about how to create this matrix A to find the eigenvalues, and how to represent the given fact that dim(im(A)) = 1.

Any tips/pointers would be helpful!

 

[Simon Bridge]

You need to review what is meant by the image and dimension of a matrix: what does rank=1 tell you?
Also - do you know of any special cases where the eigenvalues have some simple relation to the trace?
https://www.physicsforums.com/showthread.php?t=682216

Since it is 4x4 - you can always just assign 16 variables and sketch it out.
Needs lots of paper or a large whiteboard (or window).