How calculate inverse of a matrix (3*1)

Question

I'm a newbie of Matlab and non-native English language.

I have question what is inverse of matrix(3*1) such as

       1
       2
       3

I got an answer matrix(1*3)

  [1/14,   2/14,   3/14] 

by Matlab

Can you help me How can calculate by hand???

Answer 1

For non-square matrices, the inverse itself isn't well defined. Instead, you have a left inverse and a right inverse. In particular, if $A$ is an $m \times n$ matrix, and $B$ and $C$ are $n \times m$ matrices with $AB = I_m$, $CA = I_n$ then $B$ is a right inverse of $A$ and $C$ is a left inverse. The answer matlab seems to have given you is the left inverse, and is of course not unique.