Why we take transpose of Vector (Displacement Vector)?

Question

I'm trying to understand some equations that involves transpose of vectors (displacement vectors to be precise)

Two set of vectors F and G (with i,j) that corresponds to X,Y value in plane

and Final Displacement Vectors set U is calculated like this

I'm unable to understand this T in equation ? Is it Transpose ? If its transpose why we are using it, how transpose is helping us? How its calculated ? Can anyone tell me

Answer 1

It is the same as column vector. To save space its written as Tranposed row vector