Give Examples of the following( NO JUSTIFICATION NEEDED): a/ A vector space V an

Question

Give Examples of the following( NO JUSTIFICATION NEEDED):

a/ A vector space V and two distinct subspaces W1 and W2 of V that are isomorphic.

b/ Two continious real-valued functions on the interval [0,1] that are not polynomial functions but are linearly independent

c/ An infinite dimension vector space V and two subspaces W1 and W2 of V with W1 a nonzero finite dimensional subspace and W2 an infinite dimensional subspace different from V.

d/ A non zero linear transformation between two non zero vector spaces that is neither one-to-one nor onto.

Explanation / Answer

I have written the answer on a paper and uploaded it as 2 pictures at the following links:

PArt-1: http://i.imgur.com/vd1idC3.jpg

PArt-2: http://i.imgur.com/kcUML8f.jpg

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