Basis of kernel and image of a linear transformation. (All worked out)

[sid9221]

http://dl.dropbox.com/u/33103477/linear%20transformations.png

My solution(Ignore part (a), this part (b) only)

http://dl.dropbox.com/u/33103477/1.jpg
http://dl.dropbox.com/u/33103477/2.jpg

So I have worked out the basis and for the kernel of L1 and image of L2, so I have U1 and U2.

Is what I have so far correct, and how do I proceed to find the Union and Sum of the two.

PS: This is a past exam paper for which I preparing, so it's not like I'm just getting my coursework done here..

 

[sunjin09]

The (direct) sum is very simple, it is spanned by the union of the two sets of bases. The intersection is given by {x|x=L1*a=L2*b for some a, b}, i.e., x is both a linear combination of basis of L1 and a (different) linear combination of basis of L2.