Proving W is a Subspace of V: Let u & v be Vectors in V

[ECE]

Let u and v be (fixed) vectors in the vector space V. Show that the set W of all linear combinations au+bv of u and v is a subspace of V.

I cannot prove the above proof properly. Can anyone help.

-Thanks

 

[radou]

Let u and v be (fixed) vectors in the vector space V. Show that the set W of all linear combinations au+bv of u and v is a subspace of V.

I cannot prove the above proof properly. Can anyone help.

-Thanks

Take two vectors from W, and show that their linear combination is also in W.

 

[HallsofIvy]

"Take two vectors from W" means taking two linear combinations, perhaps with different "a" and "b', say au+ bv and cu+ dv. "Their linear combination" would be something like x(au+ bv)+ y(cu+ dv) for numbers, x and y. "Show it is also in W" means "show it satisfies the definition of W". Here that means show that it also can be written au+ bv for some choices of a and b.

 

[ECE]

Thanks i understand it now