1. The following set S of 2X2 matrices spans some space. Find a subset of S that forms a basis for the same space.
S={ [1 0 , [ 1 1 , [ 0 1 , [ -1 1 , [ 0 0 }
3 -1] 1 1 ] 0 1 ] -1 1] 0 3]
2. Consider the set of all elements of R^3 of the form (a,b,a+2b). Prove whether the subset is a subspace of the vector space R^3 or not.
Use "regula" addition and scalar multiplication.