How are vector spaces viewed as universal algebras?

Vector spaces spanning Question?

• Prove the following vector subspaces V and W of R^3 are equal: ...............( 1 ) ( 4 ) V=span ( 2 ) , ( 5 ) .............. ( 3 ) ( 6 ) ..................( 0 ) ( 1 ) ( 5 ) W= span ( 2 ) , ( 0 ) , ( 7 ) .................. ( 4 ) (-1 ) ( 9 ) Really need some help with this. Thanks in advance :)

• Answer:

  To prove two vector subspaces are equal its sufficient to prove dim(V) =dim(W) dim(V) = 2 To prove dim(W) =2 Show that (5,7,9) is linear combination of (0,2,4) and (1,0,-1) w1 (0,2,4) + w2(1,0,-1) = (5,7,9) w2 = 5 ......................... 1 2w1 = 7 ......................... 2 4w1-w2 =9 .......................... 3 1 and 2 give 3 Hence proved. dim(W) =2 = dim(V)