- #1

- 241

- 0

Suppose V is a vector space over R and [tex]U_1, U_2, W [/tex] are subspaces of V.

Prove or contradict:

1. [tex] W \cap (U_1+U_2) = (W \cap U_1)+(W \cap U_2)[/tex]

2. [tex] If\ U_1 \oplus W = U_2 \oplus W\ then\ U_1=U_2 [/tex]

I'm not sure how to approach this problem, and will appreciate any guidance.

Thanks!

(For the first one I had an idea to use theorem which links between dimension and subspaces equivalence, but both sides of the equation are to complex)

Prove or contradict:

1. [tex] W \cap (U_1+U_2) = (W \cap U_1)+(W \cap U_2)[/tex]

2. [tex] If\ U_1 \oplus W = U_2 \oplus W\ then\ U_1=U_2 [/tex]

I'm not sure how to approach this problem, and will appreciate any guidance.

Thanks!

(For the first one I had an idea to use theorem which links between dimension and subspaces equivalence, but both sides of the equation are to complex)

Last edited: