Given is a vector $v=\begin{pmatrix}2,&-1,&0,&1\end{pmatrix}$ as the shortest vector of the lattice $\Lambda (B)$, where $B$ is determined as $B=\begin{pmatrix}4 &-3 & 2 & 0\\ -2 &3 &1 &1 \\ -1 &5 &0 &0 \\ 7 &-2 &1 &0 \end{pmatrix}$. Find the closest vector to $t=\begin{pmatrix}-2, & 3, & 1\end{pmatrix}$ in $\Lambda (B')$, if $B'=\begin{pmatrix}7 & -2 & 1 \\ -1 & 5 & 0\\ 4 & -3 &2 \end{pmatrix}$. Prove the result.
May i ask you for an idea how to solve this problem? Or i'd be happy with an example, where i can see how to solve such problems. In the lecture we did not make any examples of CVP and SVP. I am familiar with the LLL-algorithm, i guess we need to use it for the matrices $B$ and $B'$ (the base vectors are given as rows here). Can anybody help me with this problem, please?
Thank you in advance!