Find a set of vectors $\backslash$left$\backslash$lbrace $\backslash$vec$\{$u$\},\backslash$vec$\{$v$\}\backslash$right$\backslash$rbrace in $\{\backslash$mathbb R$\}^4$ that spans the solution set of the equations

$\backslash$left$\backslash$lbrace

$\backslash$begin$\{$array$\}\{$rcl$\}$

w$-$x$+$y$+4$z & $=$ & $0,\backslash \backslash$

$4$w$+2$x$+$y & $=$ & $0.$

$\backslash$end$\{$array$\}$

$\backslash$right$.$

$\backslash$vec$\{$u$\}=\backslash$left$[\backslash$vrule width $0$pt height $4$em depth $0$pt$\backslash$right$.$

$\backslash$left$]\backslash$vrule width $0$pt height $4$em depth $0$pt$\backslash$right$.,\backslash$vec$\{$v$\}=\backslash$left$[\backslash$vrule width $0$pt height $4$em depth $0$pt$\backslash$right$.$