Question

I need to decompose a matrix of order 2x2 into the products of (2x1) and (1x2). can you please suggest a method to obtain the above result

Answer 1

You can't always do this since this factorization would imply your matrix is singular. The columns of your 2x2 matrix would have to be multiples of the same initial column (your 2x1 matrix factor) for this to be possible. If this is the case, then you can just pick a column in the (1D) column space of your 2x2 matrix as your 2x1 matrix and then choose appropriate multipliers of that column as your 1x2 matrix.