first we build up stiffness matrix then eliminate rigid body mechanisms then inverse it to find flexibility matrix.the reason we use first modes is the ratio of their participant.

first build the matrix then select what you want to be rigidity and at lest inverse the matrix to fined flexibility 

Hi

I believe you can find explained what you are looking for here.

https://en.wikipedia.org/wiki/Vibration#Multiple_degrees_of_freedom_systems_and_mode_shapes

Modal summation is covered at the lower part of the page.

Sincerely

Claes