00:01
Hi, in this question we need to let lv2w is the linear transformation of vector space.
00:22
Also given that u is the subset of w is the subspace of w.
00:34
Here we need to let u l inverse of u equals v belongs to v, l of v belongs to u.
00:49
We have to show that l inverse of u is a subspace of v or not a subspace of v.
00:56
So first we need to know l of 0 equals 0 which is belongs to u.
01:03
So 0 must be belongs to l inverse of u.
01:07
So we need to let x, y belongs to l inverse of 0.
01:13
L of x and l of y must be belongs to u.
01:17
So that we can conclude that u is a subspace of w.
01:28
Then we can write it as l of x plus l of y belongs to u which implies l of x plus y which is belongs to u which implies x plus y belongs to l inverse of u.
01:49
Hence conclude that by using the addition property we can conclude that l inverse of u is closed under addition...