Linear Algebra partitioned matrix and vector theoretical question

[Guidenable]

Homework Statement

Let X be an invertible 2011 X 2011 matrix, let I be the 2011 identity matrix.

Let B=[[X,I],[I,X^-1]] and let p=e1+e2+e3+...+e2011.

(The terms in the square brackets represent the rows of the matrix, so [X,I] is the first row)

Find a non-zero vector q, such that Bq=0.

Use partitioned matrix notation to write q explicitly in terms of p , and to display the calculation which shows that Bq=0.

The Attempt at a Solution

None. I have no idea what to do. The only thing that stands out to me is that
q is a 4022 X 1 vector and that p is a 2011 X 1 vector, so q must look something like:

q=([tp],[sp]) where t and s are real numbers

 

[kurt.physics]

. I'm not sure what to do with this information, or how to proceed with the calculation. Any help would be greatly appreciated. Thank you!