If you want to assign the value of the vector or matrix "a" to a particular column of the matrix variable "A", then
Of course, the number of rows in "A" needs to be the same as the number of elements in "a".
If you have variable "a" in the workspace, it is already "saved" in a sense that you don't need to "write" it to another variable to "save" it.
If for some reason, the value of "a" is going to be changed during data processing and you want to keep a copy of the value of "a", simply assign it to a new variable, such as a_backup=a;
You can save the numeric data "a" in a .mat file or .txt file using save().
save 'test.mat' a
save 'test.txt' a -ascii