Suppose U and W are subspaces of a vector space VSolutionSo

Suppose U and W are subspaces of a vector space V.

Solution

So, I know that W + W = W. And it makes sense that there is no counterargument that the claim isn\'t true.

So, here is my attempt:

Claim: U+W= U+W

Proof:

given U W ={0}

there is are common bases

basis of U+W = { u1,u2,u3......................un} + {w1,w2,.........................wm}

= { u1,u2.........un, w1,w2,...............wm}

L.H.S = R,H.S

hence proved