What Are the Steps to Add Vectors in Bra-Ket Notation?

[ptabor]

I'm supposed to perform the following operations.

|A + B> and <A + B|, where A and B are two vectors.

A = 3i |x> - 7i |y>
B = - |x> + 2i |y>

where |x> and |y> are orthonormal.

Little lost here... Is this asking me to add them component wise? ie
|A + B> = (3i - 1) |x> + (2i - 7i) |y>
?

and what is the meaning of the Ket-Bra notation?

 

[ptabor]

ahh, nevermind. I need to put them into row-column form.