Can anyone explain why (linear algebra)

[frasifrasi]

Why for the subspaces V and W in R^n , the

union of V and W is not a subspace of R^n?

Thank you.

 

[Vid]

Look at some examples to see why such as the union of two lines through the origin in R^2.

 

[HallsofIvy]

If v is in subspace V and w is in subspace W, it is not, in general, true that v+ w is in V$\cup$W. You can give a specific counter example by using Vid's suggestion. Let V= {(x,y)| y= x}, v= (1, 1), W= {(x,y)|y= -x}, w= (-1, 1). Is v+ w in the union of V and W?