HI! friends i need help to solve this exercise, i don't know how to do, so help me please!!:

A) V1 & V2 two vector spaces $\displaystyle V_2=<(2,-1,0,1),(1,-1,3,7)>$ and $\displaystyle V_1=\left\{\begin{array}{cc} x_1-2x_2+3x_3=0

\\ x_2-2x_3+x_4=0\end{array}\right.

$

Determine the basis for: $\displaystyle V_1\cap V_2$ y $\displaystyle V_1+V_2$.

B) From the base standard, determine the matrix of endomorphic $\displaystyle T$ characterized by verifying:

1-$\displaystyle KerT$ (core of $\displaystyle T$) is the space vector defined by the equations:

$\displaystyle KerT=\left\{\begin{array}{cc} x+y+z=0

\\ 2x-y=0\end{array}\right.

$

2-$\displaystyle (1,0,1)$ y $\displaystyle (2,1,-1)$ are eigenvectors of eigenvalues 1 and 2, respectively.

Many thanks