Mathematics - Linear Algebra - Vector spaces and subspaces - Spaces and Independence

8 problems: (1) 'Is {(x,y): x+y=0} a subspace of ℝ²? Check the 3 conditions.' (Yes). (2) 'Is {(x,y): x+y=1} a subspace?' (No, 0 not in set). (3) 'Are (1,2,3), (4,5,6), (7,8,9) linearly independent?' (No, third = 2·second - first). (4) 'Find a basis for the column space of A=[[1,2],[3,4],[5,6]].' (5)