Answer to Question #327890 in Linear Algebra for Dudu

Question

1.determine whether the set S is subspace of R⁵ defined by S={(x1,X2,X3,x4,X5)€R⁵:x1=3x2 and X3=7x4}.

2.let S be a subset of f³ defined as S={(x,y,z)€F³:x+y+2z-1=o},then determine S is a subspace of f³ or not.

3.suppose v is a subspace of v.then show that v+v=v.

4.suppose v={(x,y,x+y,x-y,2x)€f⁵:x,y€f}.find a subspace w of f⁵ such that f⁵=v©w.