What's the inverse of a 2x4 matrix?

Question

unklerhaukus · Answer

can a matrix that is not square have an inverse ?

unklerhaukus · Answer

remember $$\textbf A \textbf A^{-1}=\textbf I=\textbf A^{-1} \textbf A$$

zarkon · Answer

it could have a right invers

zarkon · Answer

*inverse

anonymous · Answer

How then is it possible to use matrices more generally in simultaneous equations (as I gather they are) without being limited to overly specific situations?

unklerhaukus · Answer

what is a right inverse @Zarkon ?

amistre64 · Answer

a matrix that is multiplied in the right sid ethat make an indentity matrix

zarkon · Answer

for an $m\times n$ matrix A ($m<n$) of full rank

you can use 

$$A^T \left(A A^T\right)^{-1}$$

anonymous · Answer

Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse. If A is m-by-n and the rank of A is equal to n, then A has a left inverse: an n-by-m matrix B such that BA = I. If A has rank m, then it has a right inverse: an n-by-m matrix B such that AB = I.

zarkon · Answer

then $$AA^T \left(A A^T\right)^{-1}=I$$

unklerhaukus · Answer

so there are two solutions to this question,