Question

Verify that W is a subspace of V, assume that V has the standard operations. W = {(x1,x2,x3,0) : x1,x2,x3 are real numbers} V=R4

Answer 1

AS [x1,x2,x3,0] +[y1,y2,y3,0] =[x1+y1,x2+y2,x3+y3,0]
this is a closed set under vector addition

As c[x1,x2,x3,0] =[cx1,cx2,cx3,0]
is also closed hence proved it is a subspace

Answer 2

thank you so much :)